A093530 Numerators of the average length of a line segment picked at random in the unit n-ball for odd n.

2, 36, 800, 1568, 290304, 123904, 15228928, 8785920, 492437504, 1608777728, 99574874112, 2508338495488, 9164554240000, 106895360655360, 31154082152448, 430159094087680, 580265191384547328, 148655260565504000, 1860654187101028352, 20860356402314477568

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Eric Weisstein's World of Mathematics, Ball Line Picking.

Example

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

Maple

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

Mathematica

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 *)

Crossrefs

Cf. A093531, A093532, A093533.

Sequence in context: A207832 A112036 A336714 * A001626 A166473 A279575

Adjacent sequences: A093527 A093528 A093529 * A093531 A093532 A093533

Keyword

nonn,frac

Author

Eric W. Weisstein, Mar 30 2004

Extensions

a(10)-a(11) from Max Alekseyev, Dec 12 2011

a(12)-a(14) from Robert G. Wilson v, Nov 04 2013

a(15)-a(20) from Alois P. Heinz, Nov 04 2013

Status

approved