A384413 Expansion of Product_{k>=1} 1/(1 - k^3 * x)^((1/6) * (2/3)^k).

1, 37, 33987, 169103895, 2499834885228, 81779253109721484, 5002571587280667349252, 513188808423273125116834036, 81795428604490137664191461936826, 19140816569244304756404266108586220066, 6295058477497449841660364475294196843864030, 2810342651288539045376339873565157506716615522598

Offset: 0

Author

Seiichi Manyama, May 28 2025

Keywords

• nonn

Crossrefs

Cf. A004123, A090351.

Programs

PARI

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

Formula

G.f.: exp((1/2) * Sum_{k>=1} b(3*k) * x^k/k), where b(n) = Sum_{k=0..n} 2^k * k! * Stirling2(n,k).