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A093530
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Numerators of the average length of a line segment picked at random in the unit n-ball for odd n.
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3
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2, 36, 800, 1568, 290304, 123904, 15228928, 8785920, 492437504, 1608777728, 99574874112, 2508338495488, 9164554240000, 106895360655360, 31154082152448, 430159094087680, 580265191384547328, 148655260565504000, 1860654187101028352, 20860356402314477568
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OFFSET
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1,1
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LINKS
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EXAMPLE
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2/3, 128/(45*Pi), 36/35, 16384/(4725*Pi), 800/693, ...
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MAPLE
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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) );
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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