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 A375424 #10 Aug 14 2024 23:14:23
%S A375424 1,1,5,17,101,589,4369,35125,323273,3263129,36301661,439023001,
%T A375424 5748342445,80949641317,1220505157481,19615065647549,334764933094289,
%U A375424 6046684538094385,115242737561241013,2311256839666971169,48658040610273601781,1072909782649220737661
%N A375424 Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x)^2.
%F A375424 a(n) = (-1)^n * n! * Sum_{k=0..n} binomial(k-2,n-k)/k!.
%F A375424 a(n) = n*a(n-1) + 3*(n-1)*a(n-2) - 2*(n-1)*(n-2)*a(n-3).
%o A375424 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x))/(1-x)^2))
%o A375424 (PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(k-2, n-k)/k!);
%Y A375424 Cf. A375409, A375425.
%Y A375424 Cf. A000255, A077880.
%K A375424 nonn
%O A375424 0,3
%A A375424 _Seiichi Manyama_, Aug 14 2024