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 A319575 #24 Feb 20 2024 09:40:14
%S A319575 0,2,4,6,24,90,252,574,1136,2034,3380,5302,7944,11466,16044,21870,
%T A319575 29152,38114,48996,62054,77560,95802,117084,141726,170064,202450,
%U A319575 239252,280854,327656,380074,438540,503502,575424,654786,742084,837830,942552,1056794,1181116
%N A319575 a(n) = (2/3)*n*(n^3 - 6*n^2 + 11*n - 3).
%H A319575 Seiichi Manyama, <a href="/A319575/b319575.txt">Table of n, a(n) for n = 0..10000</a>
%H A319575 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A319575 a(n) = [x^4] JacobiTheta3(x)^n.
%F A319575 a(n) = A319574(n,4).
%F A319575 From _Colin Barker_, Oct 02 2018: (Start)
%F A319575 G.f.: 2*x*(1 + x)*(1 - 4*x + 7*x^2) / (1 - x)^5.
%F A319575 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. (End)
%p A319575 a := n -> (2/3)*n*(n^3 - 6*n^2 + 11*n - 3):
%p A319575 seq(a(n), n=0..38);
%t A319575 A319575[n_] := 2/3*n*(n^3-6*n^2+11*n-3); Array[A319575, 50, 0] (* or *)
%t A319575 LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2, 4, 6, 24}, 50] (* _Paolo Xausa_, Feb 20 2024 *)
%o A319575 (PARI) concat(0, Vec(2*x*(1 + x)*(1 - 4*x + 7*x^2) / (1 - x)^5 + O(x^40))) \\ _Colin Barker_, Oct 02 2018
%Y A319575 Cf. A000012 (m=0), A005843 (m=1), A046092 (m=2), A130809 (m=3), this sequence (m=4), A319576 (m=5), A319577 (m=6).
%Y A319575 Column n=4 of A122141.
%Y A319575 Cf. A319574.
%K A319575 nonn,easy
%O A319575 0,2
%A A319575 _Peter Luschny_, Oct 01 2018