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 A375412 #10 Aug 14 2024 09:10:58
%S A375412 1,1,4,6,36,60,840,3360,48720,317520,4112640,36923040,503616960,
%T A375412 5976210240,89132883840,1287955468800,21130876166400,353720208441600,
%U A375412 6424780602240000,121392008337600000,2435685015296332800,51056321187692620800,1124423866880349235200
%N A375412 Expansion of e.g.f. exp(x^2 * (1 - x)) / (1 - x).
%F A375412 a(n) = (-1)^n * n! * Sum_{k=0..floor(n/2)} binomial(k-1,n-2*k)/k!.
%F A375412 D-finite with recurrence a(n) -n*a(n-1) +2*(-n+1)*a(n-2) +5*(n-1)*(n-2)*a(n-3) -3*(n-1)*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Aug 14 2024
%o A375412 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2*(1-x))/(1-x)))
%o A375412 (PARI) a(n) = (-1)^n*n!*sum(k=0, n\2, binomial(k-1, n-2*k)/k!);
%Y A375412 Cf. A375409, A375414.
%K A375412 nonn
%O A375412 0,3
%A A375412 _Seiichi Manyama_, Aug 14 2024