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 A357296 #19 Jul 31 2023 02:25:39
%S A357296 1,3,7,31,121,851,5041,43261,369601,3748249,39916801,490801081,
%T A357296 6227020801,87861842641,1310800947457,21018206008801,355687428096001,
%U A357296 6419518510204801,121645100408832001,2435836129700029057,51102829650622464001,1124549558817839481601
%N A357296 Expansion of e.g.f. Sum_{k>0} x^k / (k! * (1 - x^k/k)).
%F A357296 a(n) = n! * Sum_{d|n} 1 / (d^(n/d-1) * d!).
%F A357296 If p is prime, a(p) = 1 + p! = A038507(p).
%t A357296 a[n_] := n! * DivisorSum[n, 1/(#^(n/#-1) * #!) &]; Array[a, 20] (* _Amiram Eldar_, Jul 31 2023 *)
%o A357296 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k!*(1-x^k/k)))))
%o A357296 (PARI) a(n) = n!*sumdiv(n, d, 1/(d^(n/d-1)*d!));
%Y A357296 Cf. A038507, A057625, A327578, A354891.
%K A357296 nonn
%O A357296 1,2
%A A357296 _Seiichi Manyama_, Feb 23 2023