This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A291911 #12 Feb 16 2025 08:33:51
%S A291911 0,0,36,3456,77040,800640,5265540,25514496,99320256,327836160,
%T A291911 951285060,2488844160,5980596336,13384215936,28197301860,56398325760,
%U A291911 107825391360,198142765056,351580800996,604675808640,1011282960240,1649187872640,2628701385156
%N A291911 Number of 5-cycles in the n X n rook complement graph.
%H A291911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A291911 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A291911 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).
%F A291911 a(n) = (n - 2)^2*(n - 1)^2*n^2*(4 + 2*n + 3*n^2 - 4*n^3 + n^4)/10.
%F A291911 a(n) = 11*a(n-1) - 55*a(n-2) + 165*(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).
%F A291911 G.f.: -((36 x^3 (1 + 85 x + 1139 x^2 + 3815 x^3 + 3815 x^4 + 1139 x^5 + 85 x^6 + x^7))/(-1 + x)^11).
%t A291911 Table[(n - 2)^2 (n - 1)^2 n^2 (4 + 2 n + 3 n^2 - 4 n^3 + n^4)/10, {n, 20}]
%t A291911 LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {0, 0, 36, 3456, 77040, 800640, 5265540, 25514496, 99320256, 327836160, 951285060}, 20]
%t A291911 CoefficientList[Series[-((36 x^2 (1 + 85 x + 1139 x^2 + 3815 x^3 + 3815 x^4 + 1139 x^5 + 85 x^6 + x^7))/(-1 + x)^11), {x, 0, 20}], x]
%Y A291911 Cf. A179058 (3-cycles), A291910 (4-cycles), A291912 (6-cycles).
%K A291911 nonn
%O A291911 1,3
%A A291911 _Eric W. Weisstein_, Sep 05 2017