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 A370608 #10 Feb 23 2024 09:02:34
%S A370608 1,2,3,10,25,156,721,5356,40881,366850,3628801,40048086,479001601,
%T A370608 6228391456,87184121025,1307724593176,20922789888001,355689166978146,
%U A370608 6402373705728001,121645161595446490,2432902128489747201,51090943465394571376,1124000727777607680001
%N A370608 a(n) = (n-1)! * Sum_{d|n} 1/((d-1)! * (n/d)!^(d-1)).
%F A370608 If p is prime, a(p) = 1 + (p-1)!.
%F A370608 E.g.f.: Sum_{k>0} (k-1)! * (exp(x^k/k!)-1).
%o A370608 (PARI) a(n) = (n-1)!*sumdiv(n, d, 1/((d-1)!*(n/d)!^(d-1)));
%o A370608 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k-1)!*(exp(x^k/k!)-1))))
%Y A370608 Cf. A005225, A087906.
%Y A370608 Cf. A370603.
%K A370608 nonn
%O A370608 1,2
%A A370608 _Seiichi Manyama_, Feb 23 2024