A201059 Denominator of binomial(2n,n)/(2n).

1, 2, 3, 4, 5, 1, 7, 8, 9, 5, 11, 6, 13, 7, 1, 16, 17, 3, 19, 2, 7, 11, 23, 4, 25, 13, 27, 1, 29, 15, 31, 32, 11, 17, 5, 18, 37, 19, 39, 4, 41, 1, 43, 11, 1, 23, 47, 8, 49, 25, 17, 13, 53, 9, 55, 14, 19, 29, 59, 5, 61, 31, 21, 64, 13, 1, 67, 34, 23, 7, 71, 4, 73, 37, 5

Offset: 1

Author

N. J. A. Sloane, Nov 26 2011

Keywords

• nonn
• frac

Comments

There is at least one published paper that refers to binomial(2n,n)/(2n) as the Catalan numbers. Of course the Catalan numbers are really A000108.

Examples

			1, 3/2, 10/3, 35/4, 126/5, 77, 1716/7, 6435/8, 24310/9, 46189/5, 352716/11, 676039/6, ...
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Patrick Dehornoy, On the rotation distance between binary trees, Adv. Math. 223 (2010), no. 4, 1316-1355.

Crossrefs

Cf. A000108, A201058, A268082.

Programs

Mathematica

Table[Denominator[Binomial[2n,n]/(2n)],{n,50}] (* Harvey P. Dale, Oct 04 2021 *)

PARI

a(n) = denominator(binomial(2*n,n)/(2*n)); \\ Michel Marcus, Jan 08 2024

PARI

a(n) = my(f = factor(2*n), res = 1); for(i = 1, #f~, v = val(2*n, f[i,1]) - 2*val(n, f[i, 1]) - f[i, 2]; if(v < 0, res*=f[i, 1]^(-v))); res
val(n, p) = my(r=0); while(n, r+=n\=p); r \\ David A. Corneth, Jan 10 2024

Extensions

More terms from Michel Marcus, Jan 08 2024