A364742 G.f. satisfies A(x) = 1 / (1 - x*(1 + x*A(x))^3).

1, 1, 4, 13, 50, 201, 841, 3627, 15993, 71803, 327082, 1508002, 7023446, 32995626, 156173668, 744029238, 3565030063, 17169013899, 83061503584, 403483653745, 1967217524551, 9623463731721, 47220968518786, 232354408276613, 1146254897566224, 5668118931395946

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

Prog

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

Crossrefs

Cf. A001006, A161634, A364743, A364744.

Sequence in context: A149456 A149457 A149458 * A002746 A149459 A149460

Adjacent sequences: A364739 A364740 A364741 * A364743 A364744 A364745

Keyword

nonn

Author

Seiichi Manyama, Aug 05 2023

Status

approved