A366694 G.f. satisfies A(x) = (1 + x)^2 + x*A(x)^2.

1, 3, 7, 23, 88, 363, 1576, 7091, 32768, 154588, 741442, 3604495, 17721394, 87960004, 440165522, 2218289051, 11248850578, 57354875692, 293860786178, 1512169500356, 7811933144432, 40499933496818, 210643657689644, 1098802033533295, 5747266778089846

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

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

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

Prog

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

Crossrefs

Cf. A025227, A366695.

Cf. A086616.

Sequence in context: A289317 A113860 A080355 * A100964 A080077 A096318

Adjacent sequences: A366691 A366692 A366693 * A366695 A366696 A366697

Keyword

nonn

Author

Seiichi Manyama, Oct 16 2023

Status

approved