A385311 Expansion of e.g.f. 1/(1 - 3 * x * cos(x))^(1/3).

1, 1, 4, 25, 232, 2805, 41920, 744933, 15340416, 359136073, 9419223040, 273558859409, 8714789788672, 302151400126589, 11326084055150592, 456421403198919325, 19677025400034590720, 903660903945306053137, 44042354270955276599296, 2270411632567521580120713

Offset: 0

Author

Seiichi Manyama, Jun 24 2025

Keywords

• nonn

Crossrefs

Cf. A352252, A385310.

Cf. A380017, A385305, A385307, A385309.

Cf. A007559, A185951, A352647, A385284.

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

Formula

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