%I #10 Oct 06 2019 03:52:16
%S 1,1,2,6,30,150,1020,7140,63420,611100,6625080,72875880,977213160,
%T 12876743880,190951160400,2975661889200,51767677962000,
%U 886225654314000,17136230971860000,329530590793404000,7035395004749311200,151961029211943151200
%N Expansion of e.g.f. exp(Sum_{i>=1} Sum_{j=1..i} x^(i*j) / (i*j)).
%F E.g.f.: exp(Sum_{k>=1} ceiling(A000005(k)/2) * x^k / k).
%F E.g.f.: exp(Sum_{k>=1} A038548(k) * x^k / k).
%F E.g.f.: Product_{k>=1} 1 / (1 - x^A028260(k))^(1/A028260(k)).
%t nmax = 21; CoefficientList[Series[Exp[Sum[Ceiling[DivisorSigma[0, k]/2] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%t a[n_] := a[n] = If[n == 0, 1, Sum[Ceiling[DivisorSigma[0, k]/2] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 21}]
%t nmax = 20; CoefficientList[Series[Exp[Sum[-(x^(k*(1 + k))*LerchPhi[x^k, 1, 1 + k] + Log[1 - x^k])/k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 06 2019 *)
%Y Cf. A000005, A028260, A028342, A038548, A206303, A327940.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 30 2019