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%I #13 Apr 23 2013 06:42:13
%S 1,1,1,1,1,3,1,15,3,105,12,945,60,10395,360,135135,2520,2027025,20160,
%T 34459425,181440,654729075,1814400,13749310575,19958400,316234143225,
%U 239500800,7905853580625,3113510400,213458046676875,43589145600
%N 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.
%C Answer to question of how to extend the sequence 0, 2, 2 Pi r, 4 Pi r^2, 2 Pi^2 r^3, ...
%C Volume of n-dimensional sphere of radius r is V_n*r^n - see A072345/A072346.
%C Numerator of the rational coefficient of integral_{x>0} exp(-x^2)*x^n. [_Jean-François Alcover_, Apr 23 2013]
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 10, Eq. 19.
%D 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
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Ball.html">Ball</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hypersphere.html">Hypersphere</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Four-DimensionalGeometry.html">Four-Dimensional Geometry</a>
%e Sequence of S_n's begins 0, 2, 2, 4, 2, 8/3, 1, 16/15, 1/3, 32/105, 1/12, 64/945, ...
%t f[n_] := Pi^(n/2 - Floor[n/2])*n/(n/2)!; Table[ Denominator[ f[n]], {n, 0, 30} ]
%Y Cf. A072478. A072478(n)/A072479(n) = n*A072345(n)/A072346(n).
%K nonn,frac,easy
%O 0,6
%A _N. J. A. Sloane_, Aug 02 2002
%E More terms from _Robert G. Wilson v_, Aug 18 2002
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