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

0,3

Links

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

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...

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}]

Crossrefs

Cf. A023872.

Cf. A008485, A255672, A380290.

Sequence in context: A395374 A341398 A212850 * A215115 A142128 A158966

Adjacent sequences: A386717 A386718 A386719 * A386721 A386722 A386723

Keyword

nonn

Author

Vaclav Kotesovec, Jul 31 2025

Status

approved