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 A375411 #10 Aug 14 2024 09:14:32
%S A375411 1,0,7,-16,177,-1096,10975,-94872,1101121,-11699632,151701111,
%T A375411 -1897734400,27287272177,-385421578296,6100570870927,-95315920570696,
%U A375411 1642003509857025,-27968228816277472,520462884927746791,-9551232423922438512,190797743531054785201
%N A375411 Expansion of e.g.f. exp(-x * (1 - x)^3) / (1 - x).
%F A375411 a(n) = (-1)^n * n! * Sum_{k=0..n} binomial(3*k-1,n-k)/k!.
%F A375411 D-finite with recurrence a(n) +(-n+1)*a(n-1) +7*(-n+1)*a(n-2) +15*(n-1)*(n-2)*a(n-3) -13*(n-1)*(n-2)*(n-3)*a(n-4) +4*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - _R. J. Mathar_, Aug 14 2024
%o A375411 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x*(1-x)^3)/(1-x)))
%o A375411 (PARI) a(n) = (-1)^n*n!*sum(k=0, n, binomial(3*k-1, n-k)/k!);
%Y A375411 Cf. A375409, A375410.
%K A375411 sign
%O A375411 0,3
%A A375411 _Seiichi Manyama_, Aug 14 2024