A340903 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * sigma_0(k) * a(n-k).
1, 1, 4, 20, 139, 1192, 12318, 148318, 2041754, 31616757, 544005172, 10296204096, 212589150300, 4755177958104, 114545293676588, 2956316416222300, 81386676426000157, 2380590235918735576, 73729207700492304684, 2410324868012471929670, 82944575892433740648996
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..413
Programs
-
Mathematica
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] DivisorSigma[0, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}] nmax = 20; CoefficientList[Series[1/(1 - Sum[Sum[x^(i j)/(i j)!, {j, 1, nmax}], {i, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]! -
PARI
my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, numdiv(k)*x^k/k!)))) \\ Seiichi Manyama, Mar 29 2022 -
PARI
a(n) = if(n==0, 1, sum(k=1, n, numdiv(k)*binomial(n, k)*a(n-k))); \\ Seiichi Manyama, Mar 29 2022
Formula
E.g.f.: 1 / (1 - Sum_{i>=1} Sum_{j>=1} x^(i*j) / (i*j)!).
E.g.f.: 1 / (1 - Sum_{k>=1} sigma_0(k) * x^k/k!). - Seiichi Manyama, Mar 29 2022