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

0,2

Comments

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

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

(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));

Crossrefs

Cf. A352252, A381209.

Cf. A185951.

Sequence in context: A217526 A018027 A218759 * A295499 A059413 A377118

Adjacent sequences: A381205 A381206 A381207 * A381209 A381210 A381211

Keyword

sign,new

Author

Seiichi Manyama, Feb 17 2025

Status

approved