A366236 G.f. A(x) satisfies A(x) = 1 + x + x*(1 + x)^2*A(x)^2.

1, 2, 6, 25, 110, 520, 2566, 13073, 68244, 363129, 1962304, 10739914, 59411546, 331652408, 1865903040, 10569319231, 60227702736, 345015430415, 1985747398748, 11477353063881, 66590427901454, 387685469752989, 2264180109124196, 13261401158297918

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: 2*(1+x) / (1 + sqrt(1-4*x*(1+x)^3)).

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

Prog

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

Crossrefs

Cf. A073157, A366237, A366238.

Cf. A000108.

Sequence in context: A330637 A003454 A199241 * A276277 A355862 A299098

Adjacent sequences: A366233 A366234 A366235 * A366237 A366238 A366239

Keyword

nonn

Author

Seiichi Manyama, Oct 05 2023

Status

approved