A366695 G.f. satisfies A(x) = (1 + x)^3 + x*A(x)^2.

1, 4, 11, 39, 166, 765, 3716, 18725, 96956, 512690, 2756806, 15027651, 82853678, 461215414, 2588619402, 14632777719, 83232244238, 476040155118, 2736005962314, 15793863291792, 91530881427964, 532343678619778, 3106141476531628, 18177446846299299

Offset

0,2

Links

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

Formula

G.f.: A(x) = 2*(1+x)^3 / (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. A025227, A366694.

Cf. A162481.

Sequence in context: A126758 A149258 A326423 * A149259 A050911 A149260

Adjacent sequences: A366692 A366693 A366694 * A366696 A366697 A366698

Keyword

nonn

Author

Seiichi Manyama, Oct 16 2023

Status

approved