A384408 Expansion of Product_{k>=1} 1/(1 - k^3 * x)^((1/2)^(k+1)).

1, 13, 2426, 2393226, 7056543721, 46153703519501, 564874416706639304, 11596724623199364432312, 369937054535706501459633546, 17326810763609633232550088712162, 1140582994940898154002780391375267884, 101920298764725526200442366857326292990348

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Formula

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

a(n) ~ sqrt(Pi) * 3^(3*n + 1/2) * n^(3*n - 1/2) / (sqrt(2) * exp(3*n) * log(2)^(3*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(3*k)*x^k/k)))

Crossrefs

Cf. A084784, A384410.

Cf. A249941.

Sequence in context: A096721 A301466 A229267 * A350308 A283099 A348817

Adjacent sequences: A384405 A384406 A384407 * A384409 A384410 A384411

Keyword

nonn

Author

Seiichi Manyama, May 28 2025

Status

approved