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A093530 Numerators of the average length of a line segment picked at random in the unit n-ball for odd n. 3
2, 36, 800, 1568, 290304, 123904, 15228928, 8785920, 492437504, 1608777728, 99574874112, 2508338495488, 9164554240000, 106895360655360, 31154082152448, 430159094087680, 580265191384547328, 148655260565504000, 1860654187101028352, 20860356402314477568 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Eric Weissstein'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-Fran├žois Alcover, Oct 31 2012, translated from Maple *)

CROSSREFS

Cf. A093531, A093532, A093533.

Sequence in context: A262973 A207832 A112036 * 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

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Last modified July 23 14:56 EDT 2017. Contains 289688 sequences.