A277871 a(n) = Sum_{i=0..n+1} binomial(2*n-i,n-i+1)*Catalan(i).

1, 4, 16, 66, 279, 1203, 5275, 23474, 105853, 483108, 2229253, 10390691, 48879588, 231879456, 1108473015, 5335987930, 25849521109, 125945214309, 616833862018, 3035286848660, 14999774773110, 74413424196360, 370463714276625, 1850251796668899

Offset

0,2

Comments

T(2*n+1,n) is diagonal of triangle A125177.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1381

Formula

G.f.: (4*x*(1-sqrt(1-2*(1-sqrt(1-4*x)))))/(1-sqrt(1-4*x))^3/sqrt(1-4*x)-1/x.

a(n) ~ 2^(4*n+1/2) / (sqrt(Pi) * n^(3/2) * 3^(n-3/2)). - Vaclav Kotesovec, Nov 05 2016

Mathematica

Table[Sum[Binomial[2*i, i]*Binomial[2*n-i, n-i+1]/(i+1), {i, 0, n+1}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 05 2016 *)

Prog

(Maxima)
a(n):=sum((binomial(2*i, i)*binomial(2*n-i, n-i+1))/(i+1), i, 0, n+1);
(PARI) x='x+O('x^50); Vec((4*x*(1-sqrt(1-2*(1-sqrt(1-4*x)))))/(1-sqrt(1-4*x))^3/sqrt(1-4*x)-1/x) \\ G. C. Greubel, Apr 09 2017

Crossrefs

Cf. A000108, A125177.

Sequence in context: A307878 A217632 A026762 * A082307 A099782 A109034

Adjacent sequences: A277868 A277869 A277870 * A277872 A277873 A277874

Keyword

nonn

Author

Vladimir Kruchinin, Nov 02 2016

Status

approved