A372089 G.f. A(x) satisfies A(x) = 1/( 1 - 9*x*(1 + x*A(x)) )^(1/3).

1, 3, 21, 171, 1512, 14040, 134775, 1325457, 13279329, 135014931, 1389328200, 14440275000, 151366896639, 1598281697205, 16983592285797, 181478066048739, 1948770301135167, 21018820972926429, 227600123488744275, 2473358642698093245, 26965560597470251857

Offset: 0

Author

Seiichi Manyama, Apr 17 2024

Keywords

• nonn

Crossrefs

Cf. A372003.

Programs

PARI

a(n) = sum(k=0, n, 9^k*binomial(n/3+2*k/3-2/3, k)*binomial(k, n-k)/(n-k+1));

Formula

a(n) = Sum_{k=0..n} 9^k * binomial(n/3+2*k/3-2/3,k) * binomial(k,n-k)/(n-k+1).