A356561 Expansion of e.g.f. Product_{k>0} 1/(1 - k^3 * x^k)^(1/k^3).

1, 1, 4, 18, 204, 1260, 37440, 299880, 11002320, 204860880, 6618628800, 92924647200, 8181137764800, 124123075876800, 7211104918617600, 288085376346768000, 14964000305173920000, 340302035937191328000, 42619767305209750656000

Offset: 0

Author

Seiichi Manyama, Aug 12 2022

Keywords

• nonn

Crossrefs

Cf. A294462, A294469, A356530, A356560.

Cf. A265837, A308689.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-k^3*x^k)^(1/k^3))))

PARI

a308689(n) = sumdiv(n, d, d^(3*n/d-2));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a308689(j)*v[i-j+1]/(i-j)!)); v;

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} A308689(k) * a(n-k)/(n-k)!.