A356530 Expansion of e.g.f. Product_{k>0} 1/(1 - (k * x)^k)^(1/k^k).

1, 1, 4, 18, 156, 1020, 23040, 189000, 8462160, 174741840, 8418513600, 110288455200, 26670240273600, 364684824504000, 46300470369753600, 5169242034644688000, 359472799348030368000, 7508907247291081632000, 6157317530690533823616000

Offset: 0

Author

Seiichi Manyama, Aug 10 2022

Keywords

• nonn

Crossrefs

Cf. A023882, A294462, A356487, A356529.

Programs

PARI

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

PARI

a356529(n) = (n-1)!*sumdiv(n, d, d^(n-d+1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356529(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356529(k) * binomial(n-1,k-1) * a(n-k).