OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..n} binomial(2*k-1,k)*binomial(2*n-k-1,n-k).
G.f.: A(x) = x*F'(x)/F(x), where F(x)=x*C(x)*C(x*C(x)), C(x) is g.f. of A000108.
a(n) ~ 2^(4*n-3/2) / (sqrt(Pi*n) * 3^(n-1/2)). - Vaclav Kotesovec, Jun 02 2014
MATHEMATICA
CoefficientList[Series[2*x / (Sqrt[1-4*x] + Sqrt[-1+2*Sqrt[1-4*x]] *Sqrt[1-4*x] + 8*x-2), {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 02 2014 *)
PROG
(Maxima)
a(n):=sum(binomial(2*k-1, k)*binomial(2*n-k-1, n-k), k, 0, n);
(PARI) my(x='x+O('x^50)); Vec(2*x/((1-sqrt(1-2*(1-sqrt(1-4*x))))*sqrt(1-2*(1-sqrt(1-4*x)))*sqrt(1-4*x))) \\ G. C. Greubel, Jun 01 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Jun 01 2014
STATUS
approved