This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A354338 #15 Aug 15 2022 08:32:22
%S A354338 1,4,12,41,145,742,3962,27659,215131,1996356,17300360,218809109,
%T A354338 2421142269,31105286682,427776526574,6964677268087,97708052695959,
%U A354338 1856379196278120,30362097934331500,606395795174882161,12016899266310773097,261771941015999635310
%N A354338 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * (k/d)!) )/(n-k)!.
%F A354338 a(n) = Sum_{k=1..n} A087906(k) * binomial(n,k).
%F A354338 E.g.f.: exp(x) * Sum_{k>0} (exp(x^k) - 1)/k.
%F A354338 E.g.f.: -exp(x) * Sum_{k>0} log(1-x^k)/k!.
%o A354338 (PARI) a087906(n) = n!*sumdiv(n, d, 1/(d*(n/d)!));
%o A354338 a(n) = sum(k=1, n, a087906(k)*binomial(n, k));
%o A354338 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)*sum(k=1, N, (exp(x^k)-1)/k)))
%o A354338 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-x^k)/k!)))
%Y A354338 Cf. A087906, A356009, A354341.
%K A354338 nonn
%O A354338 1,2
%A A354338 _Seiichi Manyama_, Aug 15 2022