A381208 Expansion of e.g.f. 1/(1 - x*cos(x))^2.

1, 2, 6, 18, 48, 10, -1440, -17654, -153216, -1003950, -2787840, 58057538, 1483941888, 22381115354, 245730121728, 1455189928890, -18135147970560, -856283065534046, -19218870434267136, -306007541260257422, -2933654664287354880, 20552099782407258282, 1938717354581701951488

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. A352252, A381209.

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+1)!*I^(n-k)*a185951(n, k));

Formula

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