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 A288960 #8 Feb 16 2025 08:33:48
%S A288960 0,0,60,1248,8400,35520,114660,309120,731808,1569600,3114540,5802720,
%T A288960 10261680,17367168,28310100,44674560,68527680,102522240,150012828,
%U A288960 215186400,303208080,420383040,574335300,774204288,1030860000,1357137600,1768092300,2281275360,2917032048,3698822400
%N A288960 Number of 6-cycles in the n X n rook graph.
%H A288960 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A288960 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>
%H A288960 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8, -28, 56, -70, 56, -28, 8, -1).
%F A288960 a(n) = (n-1)*(n-2)*n^2*(n+2)*(n^2+2*n-11)/6.
%F A288960 a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)+a(n-8).
%F A288960 G.f.: (12*x^3*(5+64*x+8*x^2-8*x^3+x^4))/(-1+x)^8.
%t A288960 Table[(n - 1) (n - 2) n^2 (n + 2) (n^2 + 2 n - 11)/6, {n, 20}]
%t A288960 Table[Binomial[n, 3] n (n + 2) (n^2 + 2 n - 11), {n, 20}]
%t A288960 LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {0, 0, 60, 1248, 8400, 35520, 114660, 309120}, 20]
%t A288960 CoefficientList[Series[(12 x^2 (5 + 64 x + 8 x^2 - 8 x^3 + x^4))/(-1 + x)^8, {x, 0, 20}], x]
%Y A288960 Cf. A288961 (3-cycles), A288962 (4-cycles), A288963 (5-cycles).
%K A288960 nonn,easy
%O A288960 1,3
%A A288960 _Eric W. Weisstein_, Jun 20 2017