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 A375425 #9 Aug 14 2024 23:14:19
%S A375425 1,2,9,44,277,1974,16213,148616,1512201,16872938,205031041,2694364452,
%T A375425 38080715869,575998947614,9284490424077,158882422008704,
%U A375425 2876883685233553,54953707187064786,1104409466928407161,23295036711306707228,514558774836407746341
%N A375425 Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x)^3.
%F A375425 a(n) = (-1)^n * n! * Sum_{k=0..n} binomial(k-3,n-k)/k!.
%F A375425 a(n) = (n+1)*a(n-1) + 3*(n-1)*a(n-2) - 2*(n-1)*(n-2)*a(n-3).
%o A375425 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x))/(1-x)^3))
%o A375425 (PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(k-3, n-k)/k!);
%Y A375425 Cf. A375409, A375424.
%Y A375425 Cf. A000153.
%K A375425 nonn
%O A375425 0,2
%A A375425 _Seiichi Manyama_, Aug 14 2024