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 A354844 #13 Jun 08 2022 15:39:07
%S A354844 1,3,4,29,6,1027,8,26889,272170,861851,12,515592013,14,1530809295,
%T A354844 668366899216,9382044672017,18,1405750464518419,20,
%U A354844 1393382139935385621,4274473667143680022,30537988748467223,24,211745638285336995840025
%N A354844 a(n) = n! * Sum_{d|n} (n/d)^d / (d! * (n/d)!).
%F A354844 E.g.f.: Sum_{k>0} (exp(k * x^k) - 1)/k!.
%F A354844 If p is prime, a(p) = 1 + p.
%t A354844 a[n_] := n! * DivisorSum[n, (n/#)^#/(#! * (n/#)!) &]; Array[a, 25] (* _Amiram Eldar_, Jun 08 2022 *)
%o A354844 (PARI) a(n) = n!*sumdiv(n, d, (n/d)^d/(d!*(n/d)!));
%o A354844 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (exp(k*x^k)-1)/k!)))
%Y A354844 Cf. A121860, A354843, A354845.
%K A354844 nonn
%O A354844 1,2
%A A354844 _Seiichi Manyama_, Jun 08 2022