A093530 - OEIS

%I #22 Nov 22 2018 02:40:58

%S 2,36,800,1568,290304,123904,15228928,8785920,492437504,1608777728,

%T 99574874112,2508338495488,9164554240000,106895360655360,

%U 31154082152448,430159094087680,580265191384547328,148655260565504000,1860654187101028352,20860356402314477568

%N Numerators of the average length of a line segment picked at random in the unit n-ball for odd n.

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

%e 2/3, 128/(45*Pi), 36/35, 16384/(4725*Pi), 800/693, ...

%p B := (z,a,b) -> z^a/a*hypergeom([a,1-b],[a+1],z);

%p av := n -> simplify( int( n*s^n*B(1-s^2/4,(n+1)/2,1/2)/B(1,(n+1)/2,1/2), s=0..2) );

%t B[z_, a_, b_] := z^a/a*HypergeometricPFQ[{a, 1 - b}, {a + 1}, z]; a[n_] := Integrate[ n*s^n*B[1 - s^2/4, (n + 1)/2, 1/2]/B[1, (n + 1)/2, 1/2], {s, 0, 2}]; Table[a[n], {n, 1, 21, 2}] // Numerator (* _Jean-François Alcover_, Oct 31 2012, translated from Maple *)

%Y Cf. A093531, A093532, A093533.

%K nonn,frac

%O 1,1

%A _Eric W. Weisstein_, Mar 30 2004

%E a(10)-a(11) from _Max Alekseyev_, Dec 12 2011

%E a(12)-a(14) from _Robert G. Wilson v_, Nov 04 2013

%E a(15)-a(20) from _Alois P. Heinz_, Nov 04 2013