A356439 Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k)^(1/k) )^(1/(1-x)).

1, 1, 6, 39, 344, 3410, 42234, 567126, 8812880, 149409144, 2793232440, 56224856160, 1234342760232, 28773852409848, 718719835537872, 19045601930731320, 534564416062012800, 15792205306586537280, 491639547448322794944, 16024048206145815040704

Offset: 0

Author

Seiichi Manyama, Aug 07 2022

Keywords

• nonn

Crossrefs

Cf. A353993, A356436, A356440.

Programs

PARI

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

PARI

a356436(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d))/k);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356436(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356436(k) * binomial(n-1,k-1) * a(n-k).