Voozh

A072479

Surface area of n-dimensional sphere of radius r is n*V_n*r^(n-1) = n*Pi^(n/2)*r^(n-1)/(n/2)! = S_n*Pi^floor(n/2)*r^(n-1); sequence gives denominator of S_n.

1, 1, 1, 1, 1, 3, 1, 15, 3, 105, 12, 945, 60, 10395, 360, 135135, 2520, 2027025, 20160, 34459425, 181440, 654729075, 1814400, 13749310575, 19958400, 316234143225, 239500800, 7905853580625, 3113510400, 213458046676875, 43589145600

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OFFSET

0,6

COMMENTS

Answer to question of how to extend the sequence 0, 2, 2 Pi r, 4 Pi r^2, 2 Pi^2 r^3, ...

Volume of n-dimensional sphere of radius r is V_n*r^n - see A072345/A072346.

Numerator of the rational coefficient of integral_{x>0} exp(-x^2)*x^n. [Jean-François Alcover, Apr 23 2013]

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 10, Eq. 19.

Dusko Letic, Nenad Cakic, Branko Davidovic and Ivana Berkovic, Orthogonal and diagonal dimension fluxes of hyperspherical function, Advances in Difference Equations 2012, 2012:22; http://www.advancesindifferenceequations.com/content/2012/1/22 - From N. J. A. Sloane, Sep 04 2012

LINKS

Table of n, a(n) for n=0..30.

Eric Weisstein's World of Mathematics, Ball

Eric Weisstein's World of Mathematics, Hypersphere

Eric Weisstein's World of Mathematics, Four-Dimensional Geometry

EXAMPLE

Sequence of S_n's begins 0, 2, 2, 4, 2, 8/3, 1, 16/15, 1/3, 32/105, 1/12, 64/945, ...

MATHEMATICA

f[n_] := Pi^(n/2 - Floor[n/2])*n/(n/2)!; Table[ Denominator[ f[n]], {n, 0, 30} ]

CROSSREFS

Cf. A072478. A072478(n)/A072479(n) = n*A072345(n)/A072346(n).

Sequence in context: A286644 A290862 A290030 * A264772 A263917 A324428