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A093527 Denominators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk. 7

%I #37 Aug 12 2022 12:37:52

%S 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,

%T 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,

%U 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

%N Denominators of even raw moments in the distribution of line lengths for lines picked at random in the unit disk.

%H Stefano Spezia, <a href="/A093527/b093527.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiskLinePicking.html">Disk Line Picking</a>

%F a(k) = Denominator[(2*Gamma[3 + n])/((2 + n)*Gamma[2 + n/2]*Gamma[3 + n/2])] for n = 2k.

%F From _Paul Barry_, Sep 11 2004: (Start)

%F a(n) = numerator((n+1)(n+2)/binomial(2(n+1), n+1));

%F a(n) = numerator(2*binomial(n+2, 2)/binomial(2(n+1), n+1)). (End)

%F a(n) = numerator((n+1)/C(n+1)). - _Paul Barry_, Nov 17 2004

%F a(n) = denominator(binomial(2n, n)/n). - _Enrique Pérez Herrero_, Oct 05 2011

%F a(n) = n/gcd(n,binomial(2n,n)). - _Peter Luschny_, Oct 05 2011

%F a(n) = denominator((n + 2)*binomial(2*n+3, n+1)/((n + 1)*(2*n + 3))). - _Stefano Spezia_, Aug 06 2022

%e 1, 128/(45*Pi), 1, 2048/(525*Pi), 5/3, 16384/(2205*Pi), ...

%p A093527 := n -> n / igcd(n,binomial(2*n,n)): # _Peter Luschny_, Oct 05 2011

%t A093527[n_]:=Denominator[Binomial[2n,n]/n]; Array[A093527,200] (* _Enrique Pérez Herrero_, Oct 05 2011 *)

%Y Cf. A093070, A093526, A093528, A093529.

%Y Second column of A098505.

%Y Cf. A000108.

%K nonn,frac

%O 0,3

%A _Eric W. Weisstein_, Mar 30 2004

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)