A367072 G.f. satisfies A(x) = 1 + x + 2*x^3*A(x)^3.

1, 1, 0, 2, 6, 6, 14, 60, 120, 216, 732, 2028, 4240, 11280, 33696, 83328, 207072, 591360, 1606752, 4102656, 11172528, 31167280, 83112000, 223249824, 619860960, 1699634784, 4603619616, 12689107200, 35170240512, 96523315200, 265883115264, 738668408064

Offset

0,4

Links

Table of n, a(n) for n=0..31.

Formula

a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*k+1,n-3*k) * A001764(k).

Prog

(PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*k+1, n-3*k)*binomial(3*k, k)/(2*k+1));

Crossrefs

Cf. A001764, A366555, A367073, A367074.

Cf. A367111.

Sequence in context: A343315 A321302 A294735 * A251548 A316785 A056136

Adjacent sequences: A367069 A367070 A367071 * A367073 A367074 A367075

Keyword

nonn

Author

Seiichi Manyama, Nov 05 2023

Status

approved