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 A370674 #8 Feb 26 2024 10:11:32
%S A370674 1,0,9,14,125,702,5047,40172,362949,3628100,39916811,478996746,
%T A370674 6227020813,87178250922,1307674370745,20922789524192,355687428096017,
%U A370674 6402373702119096,121645100408832019,2432902008136718030,51090942171709621965,1124000727777128678510
%N A370674 Expansion of Sum_{k>0} k! * x^k/(1+x^k)^(k+1).
%F A370674 a(n) = Sum_{d|n} (-1)^(d-1) * (d+n/d-1)!/(d-1)!.
%F A370674 If p is an odd prime, a(p) = p + p!.
%o A370674 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1+x^k)^(k+1)))
%o A370674 (PARI) a(n) = sumdiv(n, d, (-1)^(d-1)*(d+n/d-1)!/(d-1)!);
%Y A370674 Cf. A177249, A177251, A177253.
%Y A370674 Cf. A344777, A358411.
%K A370674 nonn
%O A370674 1,3
%A A370674 _Seiichi Manyama_, Feb 25 2024