A381286 Expansion of e.g.f. 1/(1 - sin(3*x) / 3).

1, 1, 2, -3, -48, -339, -1008, 10737, 237312, 2362041, 5432832, -318158523, -7615254528, -87216236379, 173049219072, 33959321252217, 851545449234432, 9561733579228401, -129701862228492288, -9445723672920941043, -239815723596207095808, -2109465061216228379619

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• sign

Crossrefs

Cf. A000111, A381285.

Cf. A136630, A352638, A381278.

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!*(3*I)^(n-k)*a136630(n, k));

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-9)^k * binomial(n,2*k+1) * a(n-2*k-1).

a(n) = Sum_{k=0..n} k! * (3*i)^(n-k) * A136630(n,k), where i is the imaginary unit.