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 A358411 #13 Aug 30 2023 02:00:53
%S A358411 1,4,9,34,125,762,5047,40468,362949,3629560,39916811,479007174,
%T A358411 6227020813,87178331590,1307674370745,20922790251808,355687428096017,
%U A358411 6402373709377404,121645100408832019,2432902008216565330,51090942171709621965,1124000727778086681754
%N A358411 a(n) = Sum_{d|n} (d + n/d - 1)!/(d - 1)!.
%F A358411 G.f.: Sum_{k>0} k! * x^k/(1 - x^k)^(k+1).
%F A358411 If p is prime, a(p) = p + p!.
%t A358411 a[n_] := DivisorSum[n, (# + n/# - 1)!/(# - 1)! &]; Array[a, 22] (* _Amiram Eldar_, Aug 30 2023 *)
%o A358411 (PARI) a(n) = sumdiv(n, d, (d+n/d-1)!/(d-1)!);
%o A358411 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1-x^k)^(k+1)))
%Y A358411 Cf. A081543, A358389, A358410.
%K A358411 nonn
%O A358411 1,2
%A A358411 _Seiichi Manyama_, Nov 14 2022