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

0,3

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

Cf. A093070, A093526, A093528, A093529.

Second column of A098505.

Cf. A000108.

Sequence in context: A129538 A076934 A111701 * A088233 A056008 A074830

Adjacent sequences: A093524 A093525 A093526 * A093528 A093529 A093530

Keyword

nonn,frac

Author

Eric W. Weisstein, Mar 30 2004

Status

approved