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 A300847 #13 Feb 16 2025 08:33:53
%S A300847 0,0,0,0,0,12,72,252,672,1512,3024,5544,9504,15444,24024,36036,52416,
%T A300847 74256,102816,139536,186048,244188,316008,403788,510048,637560,789360,
%U A300847 968760,1179360,1425060,1710072,2038932,2416512,2848032,3339072,3895584,4523904,5230764
%N A300847 a(n) = 12*binomial(n, 5).
%C A300847 Also the number of 5-cycles in the complete graph K_n for n >= 1.
%H A300847 F. Harary, B. Manvel, <a href="http://dml.cz/dmlcz/126802">On the number of cycles in a graph</a>, Matemat. casop. 21 (1971) 55-63, Theorem 2 for 5-cycles in complete graph.
%H A300847 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CompleteGraph.html">Complete Graph</a>
%H A300847 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A300847 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A300847 G.f.: 12*x^5/(x - 1)^6.
%F A300847 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) + 6*a(n-4) - a(n-5).
%F A300847 a(n) = A052787(n)/10 = 12*A000389(n).
%F A300847 a(n) = (n - 4)*(n - 3)*(n - 2)*(n - 1)*n/10.
%t A300847 Table[12 Binomial[n, 5], {n, 0, 20}]
%t A300847 12 Binomial[Range[0, 20], 5]
%t A300847 LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 0, 0, 12, 72}, {0, 20}]
%t A300847 CoefficientList[Series[12 x^5/(x - 1)^6, {x, 0, 20}], x]
%o A300847 (PARI) a(n) = 12*binomial(n, 5); \\ _Altug Alkan_, Mar 13 2018
%Y A300847 Cf. A000389, A052787.
%K A300847 nonn,easy
%O A300847 0,6
%A A300847 _Eric W. Weisstein_, Mar 13 2018