A385284 Expansion of e.g.f. 1/(1 - 3 * x * cos(3*x))^(1/3).

1, 1, 4, 1, -152, -3515, -54080, -671363, -2823296, 199955305, 10101514240, 323321153881, 7583054076928, 80180394219757, -4570380001660928, -409907196093564395, -20705306119297925120, -748794938843475359663, -14289862480447260852224, 610587389113316064978481

Offset: 0

Author

Seiichi Manyama, Jun 24 2025

Keywords

• sign

Crossrefs

Cf. A352252, A385283.

Cf. A007559, A185951.

Programs

PARI

a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k)*(3*I)^(n-k)*a185951(n, k));

Formula

a(n) = Sum_{k=0..n} A007559(k) * (3*i)^(n-k) * A185951(n,k), where i is the imaginary unit and A185951(n,0) = 0^n.