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 A370510 #14 Feb 20 2024 13:48:04
%S A370510 1,1,2,6,25,124,738,5136,40922,367218,3664224,40240560,482278326,
%T A370510 6263414736,87618506160,1313435465280,21003904630824,356910121855320,
%U A370510 6422020465846320,121980351190294800,2438956634267865720,51206322309647263200,1126314497201852150640
%N A370510 Expansion of Sum_{k>=0} k! * ( x * (1+x^3) )^k.
%F A370510 a(n) = Sum_{k=0..floor(n/4)} (n-3*k)! * binomial(n-3*k,k).
%o A370510 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1+x^3))^k))
%o A370510 (PARI) a(n) = sum(k=0, n\4, (n-3*k)!*binomial(n-3*k, k));
%Y A370510 Cf. A240172, A370509.
%Y A370510 Cf. A370508.
%K A370510 nonn,easy
%O A370510 0,3
%A A370510 _Seiichi Manyama_, Feb 20 2024