A366696 G.f. satisfies A(x) = (1 + x)^2 + x*A(x)^3.

1, 3, 10, 57, 378, 2730, 20853, 165592, 1353297, 11307168, 96148149, 829336122, 7238765532, 63816716547, 567425771478, 5082596905629, 45820260590481, 415423374916503, 3785371205061825, 34647928319586375, 318419608552433190, 2937021429784279707

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

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

Prog

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

Crossrefs

Cf. A366266, A366697.

Cf. A364620.

Sequence in context: A107871 A111270 A307906 * A274585 A333031 A242953

Adjacent sequences: A366693 A366694 A366695 * A366697 A366698 A366699

Keyword

nonn

Author

Seiichi Manyama, Oct 16 2023

Status

approved