A372108 G.f. A(x) satisfies A(x) = 1/( 1 - 9*x/(1 - x*A(x)) )^(1/3).

1, 3, 21, 174, 1569, 14898, 146541, 1479198, 15231207, 159338433, 1688597850, 18089117742, 195559863960, 2130853276767, 23377139412366, 258005735979357, 2862644731044960, 31912076884938312, 357256970492137149, 4014802252108301061, 45274175730663116394

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

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

Crossrefs

Cf. A372089.

Sequence in context: A228923 A287995 A257675 * A195105 A285272 A295541

Adjacent sequences: A372105 A372106 A372107 * A372109 A372110 A372111

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2024

Status

approved