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 A375410 #11 Aug 14 2024 09:16:51
%S A375410 1,0,5,-4,81,-176,2605,-8100,137249,-424576,10376181,-21429860,
%T A375410 1069514545,279470736,149969551901,616166705084,28838719110465,
%U A375410 261581059999360,7560615053166949,106911086586605244,2626348956282622481,48474495094075756880,1160413567193463596685
%N A375410 Expansion of e.g.f. exp(-x * (1 - x)^2) / (1 - x).
%F A375410 a(n) = (-1)^n * n! * Sum_{k=0..n} binomial(2*k-1,n-k)/k!.
%F A375410 D-finite with recurrence a(n) +(-n+1)*a(n-1) +5*(-n+1)*a(n-2) +7*(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 A375410 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^2)/(1-x)))
%o A375410 (PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(2*k-1, n-k)/k!);
%Y A375410 Cf. A375409, A375411.
%Y A375410 Cf. A375413, A375415.
%K A375410 sign
%O A375410 0,3
%A A375410 _Seiichi Manyama_, Aug 14 2024