A381283 Expansion of e.g.f. 1/(1 - x * cos(3*x)).

1, 1, 2, -21, -192, -1095, 7200, 243747, 3088512, 1360881, -874437120, -21701765349, -186175604736, 5870711879721, 292185085151232, 5507319584787795, -38951106749890560, -6402114772676575263, -212680600451474522112, -1602903494245708491957, 197042528380347210792960

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..20.

Formula

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

a(n) = Sum_{k=0..n} k! * (3*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!*(3*I)^(n-k)*a185951(n, k));

Crossrefs

Cf. A352252, A381282.

Cf. A185951.

Sequence in context: A037630 A037756 A037644 * A329553 A365061 A110253

Adjacent sequences: A381280 A381281 A381282 * A381284 A381285 A381286

Keyword

sign,new

Author

Seiichi Manyama, Feb 18 2025

Status

approved