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A000181 - OEIS
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <html> <head> <link rel="stylesheet" href="/styles.css"> <meta name="format-detection" content="telephone=no"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta name="keywords" content="OEIS,integer sequences,Sloane" /> <title>A000181 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A000181" function redir() { var host = document.location.hostname; if(host != "oeis.org" && host != "127.0.0.1" && !/^([0-9.]+)$/.test(host) && host != "localhost" && host != "localhost.localdomain") { document.location = "https"+":"+"//"+"oeis"+".org/" + myURL; } } function sf() { if(document.location.pathname == "/" && document.f) document.f.q.focus(); } </script> </head> <body bgcolor=#ffffff onload="redir();sf()"> <div class=loginbar> <div class=login> <a href="/login?redirect=%2fA000181">login</a> </div> </div> <div class=center><div class=top> <center> <div class=donors> The OEIS is supported by <a href="http://oeisf.org/#DONATE">the many generous donors to the OEIS Foundation</a>. </div> <div class=banner> <a href="/"><img class=banner border="0" width="600" src="/banner2021.jpg" alt="A000181 - OEIS"></a> </div> </center> </div></div> <div class=center><div class=pagebody> <div class=searchbarcenter> <form name=f action="/search" method="GET"> <div class=searchbargreet> <div class=searchbar> <div class=searchq> <input class=searchbox maxLength=1024 name=q value="" title="Search Query"> </div> <div class=searchsubmit> <input type=submit value="Search" name=go> </div> <div class=hints> <span class=hints><a href="/hints.html">Hints</a></span> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> A000181 </div> <div class=seqname> Coefficients of m茅nage hit polynomials. <br><font size=-1>(Formerly M2076 N0820)</font> </div> </div> <div class=scorerefs> 3 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>2, 15, 60, 469, 3660, 32958, 328920, 3614490, 43341822, 563144725, 7880897892, 118177520295, 1890389939000, 32130521850972, 578260307815920, 10985555094348948, 219687969344126490, 4613039009310624795, 101479234383619208204, 2333872309936442446905</div> <div class=seqdatalinks> (<a href="/A000181/list">list</a>; <a href="/A000181/graph">graph</a>; <a href="/search?q=A000181+-id:A000181">refs</a>; <a href="/A000181/listen">listen</a>; <a href="/history?seq=A000181">history</a>; <a href="/search?q=id:A000181&fmt=text">text</a>; <a href="/A000181/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>4,1</div> </div> </div> <div class=section> <div class=sectname>REFERENCES</div> <div class=sectbody> <div class=sectline>J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 197.</div> <div class=sectline>N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).</div> <div class=sectline>N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline>Sean A. Irvine, <a href="/A000181/b000181.txt">Table of n, a(n) for n = 4..250</a></div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>Conjecture: 3*(2111*n-8303)*(n-4)*(-9+2*n)^2*a(n) - (n-3)*(25332*n^4 - 377236*n^3 + 1898681*n^2 - 3320738*n + 484000)*a(n-1) - 2*(n-4)*(12140*n^4 - 118152*n^3 + 337063*n^2 - 377436*n + 225720)*a(n-2) + (1052*n^5 - 40656*n^4 + 266063*n^3 - 549153*n^2 + 49850*n + 655200)*a(n-3) +(263*n+640)*(n-3)*(-7+2*n)^2*a(n-4) = 0. - <a href="/wiki/User:R._J._Mathar">R. J. Mathar</a>, Nov 02 2015</div> <div class=sectline>Conjecture: a(n) + 2*a(n+p) + a(n+2*p) is divisible by p for any prime p > 3. - <a href="/wiki/User:Mark_van_Hoeij">Mark van Hoeij</a>, Jun 10 2019</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>A diagonal of <a href="/A058087" title="Triangle read by rows, giving coefficients of the m茅nage hit polynomials ordered by descending powers. T(n, k) for 0 <= k <= n.">A058087</a>. Cf. <a href="/A000179" title="M茅nage numbers: a(0) = 1, a(1) = -1, and for n >= 2, a(n) = number of permutations s of [0, ..., n-1] such that s(i) != i a...">A000179</a>, <a href="/A000425" title="Coefficients of m茅nage hit polynomials.">A000425</a>.</div> <div class=sectline>Sequence in context: <a href="/A084169" title="A Pell Jacobsthal product.">A084169</a> <a href="/A337905" title="The number of walks of n steps on the hexagonal lattice that start at the origin and end at the adjacent vertex (1,0).">A337905</a> <a href="/A296661" title="a(n) = (exp(k)*Gamma(1+n, k) - exp(-k)*Gamma(1+n, -k))/k! for k = 3.">A296661</a> * <a href="/A047146" title="T(n,n+1), array T as in A047140.">A047146</a> <a href="/A084187" title="First occurrence of exactly n 0's in the binary expansion of sqrt(2).">A084187</a> <a href="/A267596" title="Decimal representation of the n-th iteration of the "Rule 173" elementary cellular automaton starting with a single ON (blac...">A267596</a></div> <div class=sectline>Adjacent sequences: <a href="/A000178" title="Superfactorials: product of first n factorials.">A000178</a> <a href="/A000179" title="M茅nage numbers: a(0) = 1, a(1) = -1, and for n >= 2, a(n) = number of permutations s of [0, ..., n-1] such that s(i) != i a...">A000179</a> <a href="/A000180" title="Expansion of E.g.f. exp(-x)/(1-3x).">A000180</a> * <a href="/A000182" title="Tangent (or "Zag") numbers: e.g.f. tan(x), also (up to signs) e.g.f. tanh(x).">A000182</a> <a href="/A000183" title="Number of discordant permutations of length n.">A000183</a> <a href="/A000184" title="Number of genus 0 rooted maps with 3 faces with n vertices.">A000184</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="a sequence of nonnegative numbers">nonn</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:N._J._A._Sloane">N. J. A. Sloane</a>, <a href="/wiki/User:Simon_Plouffe">Simon Plouffe</a></div> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <div class=sectline>approved</div> </div> </div> </div> <div class=space10></div> </div> </div></div> <p> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome"><font color="red">Welcome</font></a> <a href="/wiki/Main_Page"><font color="red">Wiki</font></a> <a href="/wiki/Special:RequestAccount">Register</a> <a href="/play.html">Music</a> <a href="/plot2.html">Plot 2</a> <a href="/demo1.html">Demos</a> <a href="/wiki/Index_to_OEIS">Index</a> <a href="/webcam">WebCam</a> <a href="/Submit.html">Contribute</a> <a href="/eishelp2.html">Format</a> <a href="/wiki/Style_Sheet">Style Sheet</a> <a href="/transforms.html">Transforms</a> <a href="/ol.html">Superseeker</a> <a href="/recent">Recents</a> </div> <div class=linksbar> <a href="/community.html">The OEIS Community</a> </div> <div class=linksbar> Maintained by <a href="http://oeisf.org">The OEIS Foundation Inc.</a> </div> <div class=dbinfo>Last modified November 24 12:37 EST 2024. Contains 378082 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>