A381211 Expansion of e.g.f. 1/(1 - sin(x))^3.

1, 3, 12, 57, 312, 1923, 13152, 98697, 805632, 7102563, 67233792, 679970937, 7315786752, 83421156003, 1004860895232, 12749105088777, 169926064668672, 2373678328434243, 34676591077097472, 528758667342524217, 8400613520498491392, 138830752520282729283

Offset: 0

Author

Seiichi Manyama, Feb 17 2025

Keywords

• nonn

Crossrefs

Cf. A377530, A381207, A381209, A381210.

Cf. A136630, A185690.

Programs

PARI

a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (k+2)!*I^(n-k)*a136630(n, k))/2;

Formula

a(n) = 1/2 * Sum_{k=0..n} (k+2)! * i^(n-k) * A136630(n,k), where i is the imaginary unit.