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 A386720 #9 Jul 31 2025 08:41:54
%S A386720 1,1,19,163,1571,15276,152029,1525420,15460771,157716235,1617959044,
%T A386720 16672687769,172459185341,1789587777849,18621317408384,
%U A386720 194222638392213,2029985619026851,21256104343844595,222937740908641405,2341629730618924374,24627719497316157396,259326672761381979574
%N A386720 a(n) = [x^n] G(x)^n, where G(x) = Product_{k >= 1} 1/(1 - x^k)^(k^3) is the g.f. of A023872.
%H A386720 Vaclav Kotesovec, <a href="/A386720/b386720.txt">Table of n, a(n) for n = 0..960</a>
%F A386720 a(n) = [x^n] exp(n*Sum_{k >= 1} sigma_4(k)*x^k/k).
%F A386720 a(n) ~ c * d^n / sqrt(n), where d = 10.783710654896500462544161711323081108292517438268962307143535279238... and c = 0.2464683956609371456774144752559018514863700235623819263696832303304...
%p A386720 with(numtheory):
%p A386720 G(x) := series(exp(add(sigma[4](k)*x^k/k, k = 1..25)), x, 26):
%p A386720 seq(coeftayl(G(x)^n, x = 0, n), n = 0..25);
%t A386720 Table[SeriesCoefficient[Product[1/(1-x^k)^(n*k^3), {k, 1, n}], {x, 0, n}], {n, 0, 25}]
%t A386720 Table[SeriesCoefficient[Exp[n*Sum[DivisorSigma[4, k]*x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 25}]
%Y A386720 Cf. A023872.
%Y A386720 Cf. A008485, A255672, A380290.
%K A386720 nonn
%O A386720 0,3
%A A386720 _Vaclav Kotesovec_, Jul 31 2025