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A160694 Denominator of the 2n-th raw moment for distribution of distances between two points picked at random in the interior of a unit cube. 2
1, 2, 30, 630, 525, 13860, 6306300, 36036, 11486475, 18517590, 18828810, 3346393050, 80608703175, 93699005400, 5822723907000, 397109770457400, 99444576356125, 933643660950, 17930761819220250, 1669666080332250, 2151484006370985, 27754143682185706500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 0..100

Eric Weisstein's World of Mathematics, Cube Line Picking

EXAMPLE

1, 1/2, 11/30, 211/630, 187/525, 5899/13860, 3524083/6306300, 28603/36036, ...

MATHEMATICA

p[x_] := Piecewise[ {{-x^2*((x - 8)*x^2 + (6*x - 4)*Pi), 0 <= x <= 1}, {2*x*((x^2 - 8*Sqrt[x^2 - 1] + 3)*x^2 + 12*ArcSec[x]*x^2 + Pi*(3 - 4*x) - 4*Sqrt[x^2 - 1] - 1/2), 1 < x <= Sqrt[2]}, {x*((-x^2 + 8*Sqrt[x^2 - 2] + 6*Pi - 5)* (x^2 + 1) - 16*x*ArcCsc[Sqrt[2 - 2/x^2]] - 24*(x^2 + 1)*ArcTan[Sqrt[x^2 - 2]] + 16*x*ArcTan[x*Sqrt[x^2 - 2]]), Sqrt[2] < x < Sqrt[3]}}]; a[n_] := Integrate[x^(2n)*p[x], {x, 0, Sqrt[3]}]; Table[a[n], {n, 0, 9}] // Denominator (* Jean-Fran├žois Alcover, Dec 26 2012, after Eric W. Weisstein *)

CROSSREFS

Cf. A160693.

Sequence in context: A297490 A324957 A282733 * A278884 A013525 A270531

Adjacent sequences:  A160691 A160692 A160693 * A160695 A160696 A160697

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, May 24 2009

EXTENSIONS

Edited and a(9) added by Max Alekseyev, Feb 16 2012

a(10)-a(21) from Robert G. Wilson v, Nov 06 2013

STATUS

approved

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Last modified May 27 06:24 EDT 2019. Contains 323599 sequences. (Running on oeis4.)