A093527 Denominators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.
1, 1, 3, 2, 5, 1, 7, 4, 9, 5, 11, 3, 13, 7, 1, 8, 17, 3, 19, 1, 7, 11, 23, 2, 25, 13, 27, 1, 29, 15, 31, 16, 11, 17, 5, 9, 37, 19, 39, 2, 41, 1, 43, 11, 1, 23, 47, 4, 49, 25, 17, 13, 53, 9, 55, 7, 19, 29, 59, 5, 61, 31, 21, 32, 13, 1, 67, 17, 23, 7, 71, 2, 73, 37, 5, 19, 1, 13, 79
Offset: 0
Examples
1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ...
Links
- Stefano Spezia, Table of n, a(n) for n = 0..10000
- Eric Weisstein's World of Mathematics, Disk Line Picking
Programs
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Maple
A093527 := n -> n / igcd(n,binomial(2*n,n)): # Peter Luschny, Oct 05 2011
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Mathematica
A093527[n_]:=Denominator[Binomial[2n,n]/n]; Array[A093527,200] (* Enrique Pérez Herrero, Oct 05 2011 *)
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