A352693 -id:A352693 - cp's OEIS frontend

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

Seiichi Manyama, Mar 29 2022

nonn

Exponential transform of A001157.

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

Cf. A295739, A274804.

Cf. A001157, A294362, A352693.

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

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

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

A352841 Expansion of e.g.f. 1/(1 - Sum_{k>=1} sigma_k(k) * x^k/k!).

Original entry on oeis.org

1, 1, 7, 64, 851, 13906, 277972, 6466650, 172651643, 5186830537, 173327806752, 6373233407498, 255743444526584, 11119651415719744, 520752884139087852, 26132341317365562754, 1398900109763305183707, 79569524691656775423766

Offset: 0

Seiichi Manyama, Apr 05 2022

nonn

Cf. A340903, A340904, A352693.

Cf. A023887, A352839, A352843.

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

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

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

cp's OEIS Frontend

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

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A352841 Expansion of e.g.f. 1/(1 - Sum_{k>=1} sigma_k(k) * x^k/k!).

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