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 A381211 #11 Feb 17 2025 08:18:31
%S A381211 1,3,12,57,312,1923,13152,98697,805632,7102563,67233792,679970937,
%T A381211 7315786752,83421156003,1004860895232,12749105088777,169926064668672,
%U A381211 2373678328434243,34676591077097472,528758667342524217,8400613520498491392,138830752520282729283
%N A381211 Expansion of e.g.f. 1/(1 - sin(x))^3.
%F A381211 a(n) = 1/2 * Sum_{k=0..n} (k+2)! * i^(n-k) * A136630(n,k), where i is the imaginary unit.
%o A381211 (PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
%o A381211 a(n) = sum(k=0, n, (k+2)!*I^(n-k)*a136630(n, k))/2;
%Y A381211 Cf. A377530, A381207, A381209, A381210.
%Y A381211 Cf. A136630, A185690.
%K A381211 nonn
%O A381211 0,2
%A A381211 _Seiichi Manyama_, Feb 17 2025