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 A358594 #16 Jul 31 2023 02:25:48
%S A358594 1,4,9,52,125,1626,5047,81768,408249,7263910,39916811,990191676,
%T A358594 6227020813,174356750582,1348633786515,41861724727696,355687428096017,
%U A358594 12904788209623614,121645100408832019,4866124222538035620,51490090294307945301,2248001455555300717294
%N A358594 Expansion of e.g.f. Sum_{k>0} x^k / ((k-1)! - x^k).
%F A358594 a(n) = n! * Sum_{d|n} 1/(d-1)!^(n/d).
%F A358594 If p is prime, a(p) = p + p!.
%t A358594 a[n_] := n! * DivisorSum[n, 1/(#-1)!^(n/#) &]; Array[a, 20] (* _Amiram Eldar_, Jul 31 2023 *)
%o A358594 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/((k-1)!-x^k))))
%o A358594 (PARI) a(n) = n!*sumdiv(n, d, 1/(d-1)!^(n/d));
%Y A358594 Cf. A061095, A356668.
%K A358594 nonn
%O A358594 1,2
%A A358594 _Seiichi Manyama_, Feb 23 2023