A356408 Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k) )^(1/(1-x)).

1, 1, 5, 29, 216, 1919, 20012, 236977, 3145832, 46122546, 739703182, 12865212172, 241040899668, 4836265824740, 103410589256452, 2346358252787094, 56285005757022752, 1422783492250963296, 37790069818311971640, 1051924374853915254048

Offset: 0

Author

Seiichi Manyama, Aug 05 2022

Keywords

• nonn

Crossrefs

Cf. A007841, A356336, A356406, A356409.

Programs

PARI

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

PARI

a356406(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)^d)));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356406(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356406(k) * binomial(n-1,k-1) * a(n-k).