A367073 G.f. satisfies A(x) = 1 + 2*x + x^3*A(x)^3.

1, 2, 0, 1, 6, 12, 11, 30, 120, 252, 408, 1104, 3415, 7710, 15984, 42609, 118422, 281820, 657468, 1732008, 4608288, 11375240, 28100400, 73598112, 192776895, 487507038, 1239516384, 3241480275, 8460205842, 21733941060, 56121723411, 146904032622, 383900676120

Offset: 0

Author

Seiichi Manyama, Nov 05 2023

Keywords

• nonn

Crossrefs

Cf. A001764, A366555, A367072, A367074.

Cf. A367112.

Programs

PARI

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

Formula

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