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 A375414 #8 Aug 14 2024 08:30:34
%S A375414 1,1,2,0,24,120,1080,2520,40320,302400,4838400,33264000,498960000,
%T A375414 5448643200,98075577600,1242290649600,21620216217600,337903056691200,
%U A375414 6624678348288000,119786633597030400,2466692313845760000,50371208660957184000,1133144384491671552000
%N A375414 Expansion of e.g.f. exp(-x^3 * (1 - x)) / (1 - x).
%F A375414 a(n) = (-1)^n * n! * Sum_{k=0..floor(n/3)} binomial(k-1,n-3*k)/k!.
%o A375414 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^3*(1-x))/(1-x)))
%o A375414 (PARI) a(n) = (-1)^n*n!*sum(k=0, n\3, binomial(k-1, n-3*k)/k!);
%Y A375414 Cf. A375409, A375412.
%K A375414 nonn
%O A375414 0,3
%A A375414 _Seiichi Manyama_, Aug 14 2024