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 A381863 #42 Mar 28 2025 08:55:52
%S A381863 120,1575,10080,44380,154000,451990,1170400,2748460,5965960,12137125,
%T A381863 23383360,43006600,75988640,129645740,214472000,345209480,542187800,
%U A381863 832980995,1254434720,1855122500,2698295600,3865397250,5460218400,7613778900,10490025000
%N A381863 Number of triples of triangles that are pairwise edge-disjoint in the complete graph K_n.
%D A381863 Julian Allagan, Edge-Disjoint Triangle Packings in Complete Graphs: Recurrence Relations and Closed Formulas. A revised proof version is to submitted to a Journal.
%H A381863 Andrew Howroyd, <a href="/A381863/b381863.txt">Table of n, a(n) for n = 6..1000</a>
%H A381863 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A381863 a(n) = 120*binomial(n, 6) + 735*binomial(n, 7) + 840*binomial(n, 8) + 280*binomial(n, 9).
%F A381863 G.f.: 5*x^6*(24 + 75*x - 54*x^2 + 11*x^3)/(1 - x)^10.
%e A381863 a(6) = 120 gives the number of triples of edge-disjoint triangles in K_6.
%t A381863 a[n_] := 120*Binomial[n, 6] + 735*Binomial[n, 7] + 840*Binomial[n, 8] + 280*Binomial[n, 9];
%t A381863 sequenceValues = Table[a[n], {n, 6, 30}]
%Y A381863 Cf. A381862, A054647.
%K A381863 nonn,easy
%O A381863 6,1
%A A381863 _Julian Allagan_, Mar 08 2025