A352694 Expansion of e.g.f. exp(Sum_{k>=1} sigma_2(k) * x^k/k!).

1, 1, 6, 26, 167, 1157, 9372, 82742, 806872, 8487255, 96086764, 1159845766, 14866684968, 201266031865, 2867695938970, 42849364911878, 669517721182731, 10910196881874549, 184997231064875867, 3257297876661453487, 59443905364431491367, 1122496527274459462803

Offset: 0

Author

Seiichi Manyama, Mar 29 2022

Keywords

• nonn

Comments

Exponential transform of A001157.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..505

Crossrefs

Cf. A295739, A274804.

Cf. A001157, A294362, A352693.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sigma(k, 2)*x^k/k!))))

PARI

a(n) = if(n==0, 1, sum(k=1, n, sigma(k, 2)*binomial(n-1, k-1)*a(n-k)));

Formula

a(0) = 1; a(n) = Sum_{k=1..n} sigma_2(k) * binomial(n-1,k-1) * a(n-k).