A356336 Expansion of e.g.f. ( Product_{k>0} 1/(1-x^k)^(1/k) )^(1/(1-x)).

1, 1, 5, 29, 219, 1949, 20587, 245237, 3289577, 48670973, 788572541, 13849348105, 262283664739, 5317530185889, 114939490137235, 2636612228192969, 63955437488072593, 1634890446576454297, 43920715897460109205, 1236660724225711901749, 36412086992371220561771

Offset: 0

Author

Seiichi Manyama, Aug 04 2022

Keywords

• nonn

Crossrefs

Cf. A000005, A028342, A356297, A356335, A356337.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace((1/prod(k=1, N, (1-x^k)^(1/k)))^(1/(1-x))))

PARI

a356297(n) = n!*sum(k=1, n, sigma(k, 0)/k);
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a356297(j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A356297(k) * binomial(n-1,k-1) * a(n-k).