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 A370508 #14 Feb 20 2024 13:47:00
%S A370508 1,1,2,6,23,116,702,4944,39722,358578,3593664,39595440,475746474,
%T A370508 6190838544,86740334160,1301939398080,20842001737224,354469125185880,
%U A370508 6382790173842480,121310821042966800,2426863248540057480,50975836645480342560,1121691979824460425360
%N A370508 Expansion of Sum_{k>=0} k! * ( x * (1-x^3) )^k.
%F A370508 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-3*k)! * binomial(n-3*k,k).
%o A370508 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1-x^3))^k))
%o A370508 (PARI) a(n) = sum(k=0, n\4, (-1)^k*(n-3*k)!*binomial(n-3*k, k));
%Y A370508 Cf. A013999, A212580.
%Y A370508 Cf. A370510.
%K A370508 nonn,easy
%O A370508 0,3
%A A370508 _Seiichi Manyama_, Feb 20 2024