A056616 Numerator of binomial(2n,n)/(2n+1).

1, 2, 6, 20, 70, 252, 924, 1144, 12870, 48620, 184756, 705432, 2704156, 10400600, 40116600, 155117520, 200360130, 466721244, 9075135300, 11781754600, 137846528820, 538257874440, 140273264248, 8233430727600, 32247603683100

Offset: 0

Author

N. J. A. Sloane, Aug 28 2000

Keywords

• nonn
• frac

Comments

The denominators are given in A056617.

It is easy to type binomial(2n,n)/(2n+1) by mistake, when one really wants the Catalan numbers binomial(2n,n)/(n+1), A000108.

Differs from A000984 at positions in A101681.

Examples

			The rationals r(n) begin: 1, 2/3, 6/5, 20/7, 70/9, 252/11, 924/13, 1144/5, 12870/17, ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..1663

Crossrefs

Cf. A000984, A056617, A000108, A101681.

Programs

Maple

seq(numer(binomial(2*n,n)/(2*n+1)), n=0..50); # Robert Israel, Feb 21 2017

Mathematica

Numerator[Table[Binomial[2n,n]/(2n+1),{n,0,30}]] (* Harvey P. Dale, Jul 25 2013 *)

PARI

a(n) = numerator(binomial(2*n, n)/(2*n+1)) \\ Felix Fröhlich, Feb 21 2017

Formula

Numerators of the rationals r(n) = binomial(2n,n)/(2n+1) with G.f.: 1/(2*sqrt(x))*arcsin(2*sqrt(x)). [Vladimir Kruchinin, May 31 2013]