A384407 Expansion of Product_{k>=1} 1/(1 - k^2 * x)^((1/3) * (1/2)^(k+1)).

1, 1, 13, 533, 46091, 6868835, 1568192799, 508404298647, 222017327728032, 125619393196237384, 89384894988513559768, 78116626967146591776664, 82253687701869747574913672, 102704417752375981385023218632, 150045690407598038822943364871144, 253563964213823585133287012876023080

Offset

0,3

Links

Table of n, a(n) for n=0..15.

Formula

G.f.: exp((1/3) * Sum_{k>=1} A000670(2*k) * x^k/k).

a(n) ~ sqrt(Pi) * 2^(2*n) * n^(2*n - 1/2) / (3 * exp(2*n) * log(2)^(2*n+1)). - Vaclav Kotesovec, May 29 2025

Prog

(PARI) a000670(n) = sum(k=0, n, k!*stirling(n, k, 2));
my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, a000670(2*k)*x^k/k)/3))

Crossrefs

Cf. A000670, A227044, A384409.

Sequence in context: A300525 A295942 A297518 * A281055 A030256 A023332

Adjacent sequences: A384404 A384405 A384406 * A384408 A384409 A384410

Keyword

nonn

Author

Seiichi Manyama, May 28 2025

Status

approved