A356025 Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k!) )^(1/(1-x)).

1, 1, 5, 28, 206, 1786, 18347, 212745, 2773927, 39901109, 628298992, 10725440221, 197349522471, 3888090474399, 81659016005387, 1820049574958950, 42895622543757084, 1065460090285463634, 27811791343693345811, 760920657403831436463

Offset: 0

Author

Seiichi Manyama, Aug 04 2022

Keywords

• nonn

Crossrefs

Cf. A209902, A356009, A356336.

Programs

PARI

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

PARI

a356009(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!)));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356009(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356009(k) * binomial(n-1,k-1) * a(n-k).