A056617 Denominator of binomial(2*n,n) / (2*n+1).

1, 3, 5, 7, 9, 11, 13, 5, 17, 19, 21, 23, 25, 27, 29, 31, 11, 7, 37, 13, 41, 43, 3, 47, 49, 17, 53, 55, 57, 59, 61, 9, 65, 67, 23, 71, 73, 75, 11, 79, 81, 83, 17, 29, 89, 13, 31, 19, 97, 11, 101, 103, 35, 107, 109, 37, 113, 115, 39, 119, 121, 41, 125

Offset: 0

Author

N. J. A. Sloane, Aug 28 2000

Keywords

• nonn
• easy
• frac

Comments

The numerators are given in A056616.

Examples

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

Links

• Michel Marcus, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A056616, A000108.

Programs

Magma

[Denominator((Binomial (2*n, n)) / (2*n + 1)): n in [0..70]]; // Vincenzo Librandi, May 27 2019

Mathematica

Table[Binomial[2 n, n]/(2 n + 1), {n, 0, 70}]//Denominator (* Harvey P. Dale, May 01 2019 *)

PARI

a(n) = denominator(binomial(2*n,n) / (2*n+1)); \\ Michel Marcus, May 27 2019

Formula

a(n) = denominator(r(n)) with r(n) = binomial(2*n,n)/(2*n+1).

G.f. of r(n): 1/(2*sqrt(x))*arcsin(2*sqrt(x)). [Vladimir Kruchinin, May 31 2013]