A381276 Expansion of e.g.f. exp(x * cos(3*x)).

1, 1, 1, -26, -107, 136, 9181, 53488, -427895, -10486016, -43859879, 1373548672, 23512856797, -30564574208, -6412871847563, -73709639926784, 1060067525174929, 40587133606543360, 179320588932698929, -14474677657838059520, -306563699887974043739, 2301792469199499132928

Offset: 0

Author

Seiichi Manyama, Feb 18 2025

Keywords

• sign

Comments

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

Crossrefs

Cf. A009189, A381275.

Cf. A185951, A352643, A381283.

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, (3*I)^(n-k)*a185951(n, k));

Formula

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

a(n) = Sum_{k=0..n} (3*i)^(n-k) * A185951(n,k), where i is the imaginary unit.