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 A365604 #16 Aug 05 2025 15:56:51
%S A365604 1,5,45,610,11020,248870,6744350,213233400,7704814200,313199930400,
%T A365604 14146162064400,702826758144000,38093116667766000,2236695336601458000,
%U A365604 141433354184701746000,9582086196220281456000,692463727252196674560000
%N A365604 Expansion of e.g.f. 1 / (1 - 5 * log(1 + x)).
%F A365604 a(n) = Sum_{k=0..n} 5^k * k! * Stirling1(n,k).
%F A365604 a(0) = 1; a(n) = 5 * Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).
%t A365604 a[n_] := Sum[5^k * k! * StirlingS1[n, k], {k, 0, n}]; Array[a, 17, 0] (* _Amiram Eldar_, Sep 13 2023 *)
%t A365604 With[{nn=20},CoefficientList[Series[1/(1-5*Log[1+x]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 05 2025 *)
%o A365604 (PARI) a(n) = sum(k=0, n, 5^k*k!*stirling(n, k, 1));
%Y A365604 Column k=5 of A320080.
%Y A365604 Cf. A347022, A365601, A365602, A365603.
%Y A365604 Cf. A094418, A365588.
%K A365604 nonn
%O A365604 0,2
%A A365604 _Seiichi Manyama_, Sep 11 2023