A384409 Expansion of Product_{k>=1} 1/(1 - k^4 * x)^((1/3) * (1/2)^(k+1)).

1, 25, 91285, 3123562205, 443053422073715, 178523879060427556091, 164353348187741234196744375, 299888034255064866129187000267695, 981055599661644496521237670996742113560, 5340738663490095110375815302474169583702354680

Offset: 0

Author

Seiichi Manyama, May 28 2025

Keywords

• nonn

Crossrefs

Cf. A000670, A384407.

Programs

PARI

a000670(n) = sum(k=0, n, k!*stirling(n, k, 2));
my(N=10, x='x+O('x^N)); Vec(exp(sum(k=1, N, a000670(4*k)*x^k/k)/3))

Formula

G.f.: exp((1/3) * Sum_{k>=1} A000670(4*k) * x^k/k).