A385284 - OEIS

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

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

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.

PROG

(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));

CROSSREFS