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%I #7 Feb 22 2021 07:32:35
%S 1,1,2,8,17,87,366,1514,8770,45585,267586,1612624,11914416,73215391,
%T 522906754,4364545708,33150679697,263662491935,2151338992440,
%U 20815916251604,178593028936507,1714283809331191,15531842607259512,158682350653110712,1667852117293837230
%N E.g.f.: Product_{i>=1, j>=1} (1 + x^(i*j) / (i*j)!).
%H Vaclav Kotesovec, <a href="/A341506/b341506.txt">Table of n, a(n) for n = 0..610</a>
%F E.g.f.: Product_{k>=1} (1 + x^k / k!)^sigma_0(k).
%t nmax = 24; CoefficientList[Series[Product[(1 + x^k/k!)^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t a[n_] := a[n] = If[n == 0, 1, -(n - 1)! Sum[Sum[d DivisorSigma[0, d]/(-d!)^(k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 24}]
%Y Cf. A000005, A007837, A032315, A107742, A318694, A340903, A341505, A341876.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 13 2021
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