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 A358500 #17 Nov 24 2022 04:48:47
%S A358500 1,1,2,6,24,121,721,5042,40326,362904,3628921,39917521,479006642,
%T A358500 6227061126,87178654104,1307677996921,20922829805521,355687907102642,
%U A358500 6402379932789126,121645187587486104,2432903315854636921,51090963094539245521,1124001083465514782642
%N A358500 a(n) = Sum_{k=0..floor(n/5)} (n-5*k)!.
%H A358500 Seiichi Manyama, <a href="/A358500/b358500.txt">Table of n, a(n) for n = 0..449</a>
%F A358500 a(n) = n * a(n-1) + a(n-5) - n * a(n-6) for n > 5.
%F A358500 a(n) ~ n! * (1 + 1/n^5 + 10/n^6 + 65/n^7 + 350/n^8 + 1701/n^9 + 7771/n^10 + 34150/n^11 + 146905/n^12 + ...), the coefficients are Sum_{j=0..(k-4)/5} Stirling2(k,5*j+4). - _Vaclav Kotesovec_, Nov 24 2022
%o A358500 (PARI) a(n) = sum(k=0, n\5, (n-5*k)!);
%Y A358500 Cf. A136580, A358498, A358499.
%K A358500 nonn,easy
%O A358500 0,3
%A A358500 _Seiichi Manyama_, Nov 19 2022