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.

1, 2, 30, 630, 525, 13860, 6306300, 36036, 11486475, 18517590, 18828810, 3346393050, 80608703175, 93699005400, 5822723907000, 397109770457400, 99444576356125, 933643660950, 17930761819220250, 1669666080332250, 2151484006370985, 27754143682185706500

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-François Alcover, Dec 26 2012, after Eric W. Weisstein *)

Crossrefs

Cf. A160693.

Sequence in context: A324957 A282733 A363113 * 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