A371657 G.f. satisfies A(x) = 1 + x * A(x)^2 * (1 + A(x) + A(x)^2).

1, 3, 27, 333, 4752, 73764, 1209492, 20610693, 361403937, 6478386561, 118181952369, 2186908154748, 40949739595242, 774474351098031, 14772979729013247, 283878381945510621, 5490264493926636912, 106786725176131118523, 2087502569999563971843

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..756

Formula

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

Prog

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

Crossrefs

Cf. A107708, A156016.

Cf. A219534, A219537, A371658.

Sequence in context: A264684 A217363 A234462 * A153853 A067000 A354658

Adjacent sequences: A371654 A371655 A371656 * A371658 A371659 A371660

Keyword

nonn

Author

Seiichi Manyama, Apr 01 2024

Status

approved