OFFSET
0,3
LINKS
Stefano Spezia, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Disk Line Picking
FORMULA
a(k) = Denominator[(2*Gamma[3 + n])/((2 + n)*Gamma[2 + n/2]*Gamma[3 + n/2])] for n = 2k.
From Paul Barry, Sep 11 2004: (Start)
a(n) = numerator((n+1)(n+2)/binomial(2(n+1), n+1));
a(n) = numerator(2*binomial(n+2, 2)/binomial(2(n+1), n+1)). (End)
a(n) = numerator((n+1)/C(n+1)). - Paul Barry, Nov 17 2004
a(n) = denominator(binomial(2n, n)/n). - Enrique Pérez Herrero, Oct 05 2011
a(n) = n/gcd(n,binomial(2n,n)). - Peter Luschny, Oct 05 2011
a(n) = denominator((n + 2)*binomial(2*n+3, n+1)/((n + 1)*(2*n + 3))). - Stefano Spezia, Aug 06 2022
EXAMPLE
1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ...
MAPLE
A093527 := n -> n / igcd(n, binomial(2*n, n)): # Peter Luschny, Oct 05 2011
MATHEMATICA
A093527[n_]:=Denominator[Binomial[2n, n]/n]; Array[A093527, 200] (* Enrique Pérez Herrero, Oct 05 2011 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Eric W. Weisstein, Mar 30 2004
STATUS
approved