cp's OEIS Frontend

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.

%I A072479 #14 Feb 16 2025 08:32:46
%S A072479 1,1,1,1,1,3,1,15,3,105,12,945,60,10395,360,135135,2520,2027025,20160,
%T A072479 34459425,181440,654729075,1814400,13749310575,19958400,316234143225,
%U A072479 239500800,7905853580625,3113510400,213458046676875,43589145600
%N 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.
%C A072479 Answer to question of how to extend the sequence 0, 2, 2 Pi r, 4 Pi r^2, 2 Pi^2 r^3, ...
%C A072479 Volume of n-dimensional sphere of radius r is V_n*r^n - see A072345/A072346.
%C A072479 Numerator of the rational coefficient of integral_{x>0} exp(-x^2)*x^n. [_Jean-François Alcover_, Apr 23 2013]
%D A072479 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 10, Eq. 19.
%D A072479 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 A072479 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Ball.html">Ball</a>
%H A072479 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Hypersphere.html">Hypersphere</a>
%H A072479 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Four-DimensionalGeometry.html">Four-Dimensional Geometry</a>
%e A072479 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 A072479 f[n_] := Pi^(n/2 - Floor[n/2])*n/(n/2)!; Table[ Denominator[ f[n]], {n, 0, 30} ]
%Y A072479 Cf. A072478. A072478(n)/A072479(n) = n*A072345(n)/A072346(n).
%K A072479 nonn,frac,easy
%O A072479 0,6
%A A072479 _N. J. A. Sloane_, Aug 02 2002
%E A072479 More terms from _Robert G. Wilson v_, Aug 18 2002