A372091 G.f. A(x) satisfies A(x) = 1/( 1 - 9*x*A(x)*(1 + x*A(x)) )^(1/3).

1, 3, 30, 378, 5382, 82377, 1323153, 21998493, 375346062, 6534966438, 115634273139, 2073448947960, 37593341804520, 688026597386004, 12694000438662381, 235845671565830850, 4408763725976408766, 82861865131590443808, 1564885072909535335695

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

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

a(n) = 9^n*binomial((4*n-2)/3, n)*hypergeom([(1-n)/2, -n/2], [(2-4*n)/3], -4/9)/(n+1). - Stefano Spezia, Apr 18 2024

Prog

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

Crossrefs

Cf. A372004.

Sequence in context: A372087 A357770 A372105 * A372110 A354659 A058831

Adjacent sequences: A372088 A372089 A372090 * A372092 A372093 A372094

Keyword

nonn

Author

Seiichi Manyama, Apr 17 2024

Status

approved