A340904 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * sigma_1(k) * a(n-k).

1, 1, 5, 28, 225, 2206, 26174, 361278, 5704401, 101297701, 1998893240, 43386854622, 1027353587730, 26353742447280, 728030940612638, 21548668265211778, 680330296613877761, 22821706122361385354, 810587673640374442445, 30390159250481750866640

Offset: 0

Author

Ilya Gutkovskiy, Jan 26 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..404

Crossrefs

Cf. A000203, A006153, A180305, A274804, A340903.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] DivisorSigma[1, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[1/(1 - Sum[Sum[i x^(i j)/(i j)!, {j, 1, nmax}], {i, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, sigma(k)*x^k/k!)))) \\ Seiichi Manyama, Mar 29 2022

PARI

a(n) = if(n==0, 1, sum(k=1, n, sigma(k)*binomial(n, k)*a(n-k))); \\ Seiichi Manyama, Mar 29 2022

Formula

E.g.f.: 1 / (1 - Sum_{i>=1} Sum_{j>=1} i * x^(i*j) / (i*j)!).

E.g.f.: 1 / (1 - Sum_{k>=1} sigma_1(k) * x^k/k!). - Seiichi Manyama, Mar 29 2022