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 A356004 #11 Jul 22 2022 16:44:08
%S A356004 1,4,14,64,322,2054,14380,116722,1060580,10636042,116996464,
%T A356004 1411275650,18346583452,256869465610,3856674412952,61743633813634,
%U A356004 1049641774831780,18896533652098442,359034139389870400,7182372973523436802,150833211474559084844
%N A356004 a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d! * (k/d)!).
%F A356004 E.g.f.: (1/(1-x)) * Sum_{k>0} (exp(x^k) - 1)/k!.
%F A356004 a(n) = n! * Sum_{k=1..n} A121860(k)/k!.
%t A356004 a[n_] := n! * Sum[DivisorSum[k, 1/(#!*(k/#)!) &], {k, 1, n}]; Array[a, 21] (* _Amiram Eldar_, Jul 22 2022 *)
%o A356004 (PARI) a(n) = n!*sum(k=1, n, sumdiv(k,d,1/(d!*(k/d)!)));
%o A356004 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(x^k)-1)/k!)/(1-x)))
%Y A356004 Cf. A002627, A121860, A355886, A355991.
%K A356004 nonn
%O A356004 1,2
%A A356004 _Seiichi Manyama_, Jul 22 2022