A195686 a(n) = C(2*n,n) / gcd(n,C(2*n,n)).

1, 2, 3, 20, 35, 252, 154, 3432, 6435, 48620, 92378, 705432, 676039, 10400600, 20058300, 10341168, 300540195, 2333606220, 1512522550, 35345263800, 6892326441, 179419291480, 1052049481860, 8233430727600, 2687300306925, 126410606437752, 247959266474052

Offset: 0

Author

Peter Luschny, Oct 06 2011

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A093526, A093527, A145429.

Programs

Maple

A195686  := n -> binomial(2*n,n)/igcd(n,binomial(2*n,n));

Mathematica

a[n_] := Numerator[Binomial[2n,n]/n]; Join[{1}, Table[a[n], {n, 100}]] (* Enrique Pérez Herrero, Mar 26 2012 *)

Formula

A093526(n) = a(n+1)/(n+2).

a(n) = numerator(C(2n,n)/n). - Enrique Pérez Herrero, Mar 26 2012

Sum_{n>=0} A093527(n)/a(n+1) = Sum_{n>=1} n/binomial(2*n,n) = 2/3 + 2*Pi/(9*sqrt(3)) (A145429). - Amiram Eldar, Jan 26 2022

a(n) = numerator((n + 1)*binomial(2*n+1, n)/(n*(2*n + 1))) for n > 0. - Stefano Spezia, Aug 06 2022