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 A319576 #30 Feb 20 2024 09:36:50
%S A319576 0,0,8,24,48,112,312,840,2016,4320,8424,15224,25872,41808,64792,96936,
%T A319576 140736,199104,275400,373464,497648,652848,844536,1078792,1362336,
%U A319576 1702560,2107560,2586168,3147984,3803408,4563672,5440872,6448000,7598976,8908680,10392984
%N A319576 a(n) = (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9).
%H A319576 Seiichi Manyama, <a href="/A319576/b319576.txt">Table of n, a(n) for n = 0..10000</a>
%H A319576 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A319576 a(n) = [x^5] JacobiTheta3(x)^n.
%F A319576 a(n) = A319574(n,5).
%F A319576 From _Colin Barker_, Oct 02 2018: (Start)
%F A319576 G.f.: 8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6.
%F A319576 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.
%F A319576 (End)
%p A319576 a := n -> (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9):
%p A319576 seq(a(n), n=0..41);
%t A319576 A319576[n_] := 4/15*n*(n-1)*(n^3-9*n^2+26*n-9); Array[A319576, 50, 0] (* or *)
%t A319576 LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 8, 24, 48, 112}, 50] (* _Paolo Xausa_, Feb 20 2024 *)
%o A319576 (PARI) concat([0,0], Vec(8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6 + O(x^40))) \\ _Colin Barker_, Oct 02 2018
%Y A319576 Cf. A000012 (m=0), A005843 (m=1), A046092 (m=2), A130809 (m=3), A319575 (m=4), this sequence (m=5), A319577 (m=6).
%Y A319576 Column n=5 of A122141.
%Y A319576 Cf. A319574.
%K A319576 nonn,easy
%O A319576 0,3
%A A319576 _Peter Luschny_, Oct 01 2018