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

%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