login
A366694
G.f. satisfies A(x) = (1 + x)^2 + x*A(x)^2.
1
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
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. A086616.
Sequence in context: A289317 A113860 A080355 * A100964 A080077 A096318
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 16 2023
STATUS
approved