OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..404
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
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]!
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 26 2021
STATUS
approved