A366676 G.f. satisfies A(x) = 1 + x^3 + x*A(x)^3.

1, 1, 3, 13, 58, 288, 1512, 8250, 46296, 265491, 1548976, 9165156, 54865737, 331694167, 2022232068, 12419023617, 76755164643, 477049187268, 2979758649996, 18695276174079, 117766227611046, 744527923478730, 4722464911515423, 30044091589750350

Offset: 0

Author

Seiichi Manyama, Oct 16 2023

Keywords

• nonn

Crossrefs

Cf. A176697, A366677.

Cf. A366266, A366555.

Programs

PARI

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

Formula

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