A384358 Expansion of Product_{k>=1} 1/(1 - k*(k+1)*(k+2)*(k+3)/24 * x)^((1/162) * (2/3)^k).

1, 1, 1321, 16210201, 820657237561, 117856012064818489, 38648527065793350391329, 25112088578490906968072202609, 29248901038277816617484354852346429, 56683882435365104654655753669402941927069, 172551008002533192343018045442364399983107657925

Offset: 0

Author

Seiichi Manyama, May 27 2025

Keywords

• nonn

Crossrefs

Cf. A384362.

Programs

PARI

a384362(n, k) = sum(i=0, k*n, 2^i*sum(j=0, i, (-1)^j*binomial(i, j)*binomial(i-j, n)^k));
my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, a384362(4, k)*x^k/k)/16))

Formula

G.f.: exp((1/16) * Sum_{k>=1} A384362(4,k) * x^k/k).