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 A358498 #15 Nov 24 2022 03:37:52
%S A358498 1,1,2,7,25,122,727,5065,40442,363607,3633865,39957242,479365207,
%T A358498 6230654665,87218248442,1308153733207,20929020542665,355774646344442,
%U A358498 6403681859461207,121666029429374665,2433257782822984442,51097345853568901207,1124122393807037054665
%N A358498 a(n) = Sum_{k=0..floor(n/3)} (n-3*k)!.
%H A358498 Seiichi Manyama, <a href="/A358498/b358498.txt">Table of n, a(n) for n = 0..449</a>
%F A358498 a(n) = n * a(n-1) + a(n-3) - n * a(n-4) for n > 3.
%F A358498 a(n) ~ n! * (1 + 1/n^3 + 3/n^4 + 7/n^5 + 16/n^6 + 46/n^7 + 203/n^8 + 1178/n^9 + 7242/n^10 + ...), for coefficients see A143817. - _Vaclav Kotesovec_, Nov 24 2022
%o A358498 (PARI) a(n) = sum(k=0, n\3, (n-3*k)!);
%Y A358498 Cf. A136580, A358499, A358500.
%K A358498 nonn,easy
%O A358498 0,3
%A A358498 _Seiichi Manyama_, Nov 19 2022