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.

1, 1, 19, 163, 1571, 15276, 152029, 1525420, 15460771, 157716235, 1617959044, 16672687769, 172459185341, 1789587777849, 18621317408384, 194222638392213, 2029985619026851, 21256104343844595, 222937740908641405, 2341629730618924374, 24627719497316157396, 259326672761381979574

Offset: 0

Author

Vaclav Kotesovec, Jul 31 2025

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..960

Crossrefs

Cf. A023872.

Cf. A008485, A255672, A380290.

Programs

Maple

with(numtheory):
G(x) := series(exp(add(sigma[4](k)*x^k/k, k = 1..25)), x, 26):
seq(coeftayl(G(x)^n, x = 0, n), n = 0..25);

Mathematica

Table[SeriesCoefficient[Product[1/(1-x^k)^(n*k^3), {k, 1, n}], {x, 0, n}], {n, 0, 25}]
Table[SeriesCoefficient[Exp[n*Sum[DivisorSigma[4, k]*x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 25}]

Formula

a(n) = [x^n] exp(n*Sum_{k >= 1} sigma_4(k)*x^k/k).

a(n) ~ c * d^n / sqrt(n), where d = 10.783710654896500462544161711323081108292517438268962307143535279238... and c = 0.2464683956609371456774144752559018514863700235623819263696832303304...