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 A370603 #11 Feb 23 2024 11:01:52
%S A370603 1,4,9,40,125,936,5047,42848,367929,3668500,39916811,480577032,
%T A370603 6227020813,87197480384,1307761815375,20923593490816,355687428096017,
%U A370603 6402405005606628,121645100408832019,2432903231908929800,51090944698284691221,1124000756238680570272
%N A370603 a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)!^(d-1)).
%F A370603 a(n) = n * A370608(n).
%F A370603 If p is prime, a(p) = p + p!.
%F A370603 E.g.f.: Sum_{k>0} x^k * exp(x^k/k!).
%o A370603 (PARI) a(n) = n!*sumdiv(n, d, 1/((d-1)!*(n/d)!^(d-1)));
%o A370603 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k*exp(x^k/k!))))
%Y A370603 Cf. A370579, A370602.
%Y A370603 Cf. A370608.
%K A370603 nonn
%O A370603 1,2
%A A370603 _Seiichi Manyama_, Feb 23 2024