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 A291912 #11 Feb 16 2025 08:33:51
%S A291912 0,0,60,18336,840800,14629200,143939460,971877760,5018582016,
%T A291912 21193207200,76518984300,243664127520,699965254560,1844973808496,
%U A291912 4520720267700,10403885452800,22674321863680,47112768624960,93845538165276,180039346960800,333959821087200,600947653207440
%N A291912 Number of 6-cycles in the n X n rook complement graph.
%H A291912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A291912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookComplementGraph.html">Rook Complement Graph</a>
%H A291912 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).
%F A291912 a(n) = (-2 + n)*(-1 + n)^2*n^2*(-52 + 12*n + 76*n^2 - 63*n^3 - 2*n^4 + 20*n^5 - 8*n^6 + n^7)/12.
%F A291912 a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13).
%F A291912 G.f.: (4 x^3 (-15 - 4389 x - 151778 x^2 - 1277962 x^3 - 3535266 x^4 - 3576650 x^5 - 1293586 x^6 - 137682 x^7 - 1883 x^8 + 11 x^9))/(-1 + x)^13.
%t A291912 Table[(-2 + n) (-1 + n)^2 n^2 (-52 + 12 n + 76 n^2 - 63 n^3 - 2 n^4 + 20 n^5 - 8 n^6 + n^7)/12, {n, 20}]
%t A291912 LinearRecurrence[{13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {0, 0, 60, 18336, 840800, 14629200, 143939460, 971877760, 5018582016, 21193207200, 76518984300, 243664127520, 699965254560}, 20]
%t A291912 CoefficientList[Series[(4 x^2 (-15 - 4389 x - 151778 x^2 - 1277962 x^3 - 3535266 x^4 - 3576650 x^5 - 1293586 x^6 - 137682 x^7 - 1883 x^8 + 11 x^9))/(-1 + x)^13, {x, 0, 20}], x]
%Y A291912 Cf. A179058 (3-cycles), A291910 (4-cycles), A291911 (5-cycles).
%K A291912 nonn
%O A291912 1,3
%A A291912 _Eric W. Weisstein_, Sep 05 2017