OFFSET
0,2
FORMULA
G.f.: (g-1)^2/((1-3*g)*(g^2-3*g+1)) where g*(1-g)^2 = x. - Mark van Hoeij, Nov 10 2011
a(n) = A134511(4n,2n). - Alois P. Heinz, Mar 02 2018
a(n) = Sum_{j=0..n} binomial(4*n-j, j). - Petros Hadjicostas, Sep 04 2019
a(n) = hypergeom([1/2 - 2*n, -2*n], [-4*n], -4) - binomial(3*n - 1, n + 1)* hypergeom([1, 1 - n, 3/2 - n], [1 - 3*n, n + 2], -4) for n > 0. - Peter Luschny, Sep 04 2019
a(n) ~ 3^(3*n + 1/2) / (sqrt(Pi*n) * 2^(2*n-1)). - Vaclav Kotesovec, Sep 04 2019
MAPLE
a := n -> `if`(n=0, 1, hypergeom([1/2 - 2*n, -2*n], [-4*n], -4) - binomial(3*n - 1, n + 1)*hypergeom([1, 1 - n, 3/2 - n], [1 - 3*n, n + 2], -4)):
seq(simplify(a(n)), n = 0..24); # Peter Luschny, Sep 04 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 02 2000
STATUS
approved