A381209 Expansion of e.g.f. 1/(1 - x*cos(x))^3.

1, 3, 12, 51, 216, 735, 0, -39081, -575232, -6047973, -48314880, -189159333, 3046957056, 99745485879, 1789140627456, 23433663134655, 185580069027840, -1250544374605389, -94781673979379712, -2543434372808424957, -47763303489939701760, -586864592847636893937

Offset: 0

Author

Seiichi Manyama, Feb 17 2025

Keywords

• sign

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Cf. A377530, A381207, A381210, A381211.

Cf. A352252, A381208.

Cf. A185951.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (k+2)!*I^(n-k)*a185951(n, k))/2;

Formula

a(n) = 1/2 * Sum_{k=0..n} (k+2)! * i^(n-k) * A185951(n,k), where i is the imaginary unit.