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 A370602 #9 Feb 23 2024 11:01:47
%S A370602 1,4,9,40,125,1056,5047,51248,383049,4364020,39916811,576885552,
%T A370602 6227020813,99634224704,1334500527375,23592657488416,355687428096017,
%U A370602 7202890599354468,121645100408832019,2679832071577681040,51612375654647808021,1226182612423511392672
%N A370602 a(n) = n! * Sum_{d|n} 1/((d-1)! * (n/d)^(d-1)).
%F A370602 a(n) = n * A005225(n).
%F A370602 If p is prime, a(p) = p + p!.
%F A370602 E.g.f.: Sum_{k>0} x^k * exp(x^k/k).
%o A370602 (PARI) a(n) = n!*sumdiv(n, d, 1/((d-1)!*(n/d)^(d-1)));
%o A370602 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k*exp(x^k/k))))
%Y A370602 Cf. A370579, A370603.
%Y A370602 Cf. A005225.
%K A370602 nonn
%O A370602 1,2
%A A370602 _Seiichi Manyama_, Feb 23 2024