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 A358608 #15 Nov 25 2022 06:40:40
%S A358608 1,1,2,5,23,118,715,5017,40202,362165,3623783,39876598,478639435,
%T A358608 6223397017,87138414602,1307195728565,20916566490983,355600289681398,
%U A358608 6401066509999435,121624183842341017,2432546407886958602,51084541105199440565,1123879103593765338983
%N A358608 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-3*k)!.
%H A358608 Seiichi Manyama, <a href="/A358608/b358608.txt">Table of n, a(n) for n = 0..449</a>
%F A358608 a(n) = n * a(n-1) - a(n-3) + n * a(n-4) for n > 3.
%F A358608 a(n) ~ n! * (1 - 1/n^3 - 3/n^4 - 7/n^5 - 14/n^6 - 16/n^7 + 77/n^8 + 922/n^9 + 6660/n^10 + ...), for coefficients see A143630. - _Vaclav Kotesovec_, Nov 25 2022
%o A358608 (PARI) a(n) = sum(k=0, n\3, (-1)^k*(n-3*k)!);
%Y A358608 Cf. A358607, A358609, A358611.
%Y A358608 Cf. A143630, A358498.
%K A358608 nonn
%O A358608 0,3
%A A358608 _Seiichi Manyama_, Nov 23 2022