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 A375409 #10 Aug 14 2024 08:31:11
%S A375409 1,0,3,2,33,84,835,4542,42273,353672,3670371,39704730,480066433,
%T A375409 6221189532,87210179043,1307488285334,20923882733505,355680675491472,
%U A375409 6402415875542083,121644826003391922,2432903816934178401,51090929833475100260,1124000813126981130243
%N A375409 Expansion of e.g.f. exp(-x * (1 - x)) / (1 - x).
%F A375409 a(n) = (-1)^n * n! * Sum_{k=0..n} binomial(k-1,n-k)/k!.
%F A375409 a(n) = (n-1) * (a(n-1) + 3*a(n-2) - 2*(n-2)*a(n-3)).
%o A375409 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x))/(1-x)))
%o A375409 (PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(k-1, n-k)/k!);
%Y A375409 Cf. A375410, A375411.
%Y A375409 Cf. A375412, A375414.
%K A375409 nonn
%O A375409 0,3
%A A375409 _Seiichi Manyama_, Aug 14 2024