Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Apr 15 2022 10:08:54
%S 1,1,6,44,491,6597,110652,2144606,47988524,1206275925,33777572464,
%T 1040200674416,34967153135940,1273241146218823,49928549099500206,
%U 2097300313258417056,93953420539864844743,4470694981375022862697,225184078001798318202935
%N Expansion of e.g.f. exp(Sum_{k>=1} sigma_k(k) * x^k/k!).
%C Exponential transform of A023887.
%F a(0) = 1; a(n) = Sum_{k=1..n} sigma_k(k) * binomial(n-1,k-1) * a(n-k).
%t nmax = 20; CoefficientList[Series[E^(Sum[DivisorSigma[k, k]*x^k/k!, {k, 1, nmax}]), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Apr 15 2022 *)
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sigma(k, k)*x^k/k!))))
%o (PARI) a(n) = if(n==0, 1, sum(k=1, n, sigma(k, k)*binomial(n-1, k-1)*a(n-k)));
%Y Cf. A295739, A274804, A352694.
%Y Cf. A023887, A352841, A352842, A202477.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Apr 05 2022