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%I #8 Jul 23 2022 09:53:57
%S 1,4,15,73,390,2641,19208,164585,1541746,16158341,181370552,
%T 2283224065,30160914446,434715492485,6655132252876,109315669969217,
%U 1879289179364690,34719396682318021,666070910669770400,13590051478686198401,289043813095242038422
%N a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)!).
%F E.g.f.: (1/(1-x)) * Sum_{k>0} (exp(x^k) - 1)/k.
%F E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1-x^k)/k!.
%o (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)!)));
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(x^k)-1)/k)/(1-x)))
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k)/k!)/(1-x)))
%Y Cf. A087906, A356004.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jul 23 2022
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