A372105 G.f. A(x) satisfies A(x) = 1/( 1 - 9*x*A(x)/(1-x) )^(1/3).

1, 3, 30, 372, 5187, 77682, 1220421, 19842492, 331047138, 5635390827, 97491744102, 1709067567387, 30293505154362, 542010120629052, 9775907758416999, 177556754470826046, 3244682279388126576, 59614554914471797482, 1100573677912355195313

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} 9^k * binomial(4*k/3-2/3,k) * binomial(n-1,n-k)/(k+1).

Prog

(PARI) a(n) = sum(k=0, n, 9^k*binomial(4*k/3-2/3, k)*binomial(n-1, n-k)/(k+1));

Crossrefs

Cf. A361375, A372087.

Sequence in context: A365152 A372087 A357770 * A372091 A372110 A354659

Adjacent sequences: A372102 A372103 A372104 * A372106 A372107 A372108

Keyword

nonn

Author

Seiichi Manyama, Apr 18 2024

Status

approved