A270560 a(n) = Sum_{i=0..n/2}((binomial(2*i+1,i)*binomial(2*n+2,n-2*i))/(2*i+1)).

1, 4, 16, 64, 257, 1036, 4191, 17008, 69221, 282468, 1155493, 4737720, 19468217, 80167548, 330792264, 1367637504, 5665322405, 23512490804, 97763764907, 407238803064, 1699418247864, 7104279648480, 29750734951599, 124802322916560

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: (1/x) * (1-sqrt((2*C(x)-1)*(3-2*C(x))))/(sqrt(1-4*x)*(C(x)-1)*2), where C(x) is g.f. of Catalan numbers (A000108).

a(n) ~ 3^(2*n + 7/2) / (sqrt(Pi) * n^(3/2) * 2^(n + 3/2)). - Vaclav Kotesovec, Mar 19 2016

Maple

A270560 := proc(n)
    add(binomial(2*i+1, i)/(2*i+1)*binomial(2*n+2, n-2*i), i=0..n/2) ;
end proc: # R. J. Mathar, Jun 07 2016

Mathematica

Table[Sum[Binomial[2*i+1, i]*Binomial[2*n+2, n-2*i]/(2*i+1), {i, 0, n/2}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 19 2016 *)

Prog

(Maxima)
a(n):=sum((binomial(2*i+1, i)*binomial(2*n+2, n-2*i))/(2*i+1), i, 0, (n)/2);
(PARI) a(n) = sum(i=0, n\2, (binomial(2*i+1, i)*binomial(2*n+2, n-2*i))/(2*i+1)); \\ Michel Marcus, Mar 19 2016

Crossrefs

Cf. A000108.

Sequence in context: A238940 A083589 A098590 * A071357 A142872 A113995

Adjacent sequences: A270557 A270558 A270559 * A270561 A270562 A270563

Keyword

nonn

Author

Vladimir Kruchinin, Mar 18 2016

Status

approved