A371610 G.f. satisfies A(x) = ( 1 + x * (1 + x*A(x)^3)^2 )^2.

1, 2, 5, 30, 162, 996, 6449, 43086, 296750, 2086244, 14920110, 108202326, 793793106, 5880645408, 43931188235, 330570658228, 2503247547204, 19061888196960, 145874708874538, 1121290880430144, 8653411948545596, 67022656919955620, 520808586384360885

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(2*k,n-k)/(3*(n-k)+1).

G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A137967.

Prog

(PARI) a(n, r=2, s=2, t=0, u=6) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A137967, A371615.

Sequence in context: A163800 A180826 A367521 * A209325 A019027 A019031

Adjacent sequences: A371607 A371608 A371609 * A371611 A371612 A371613

Keyword

nonn

Author

Seiichi Manyama, Mar 29 2024

Status

approved