Search: id:A072346
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%I A072346
%S A072346 1,1,1,3,2,15,6,105,24,945,120,10395,720,135135,5040,2027025,40320,34459425,
%T A072346 362880,654729075,3628800,13749310575,39916800,316234143225,479001600,
               7905853580625,
%U A072346 6227020800,213458046676875,87178291200,6190283353629375,1307674368000
%N A072346 Volume of n-dimensional sphere of radius r is V_n*r^n = Pi^(n/2)*r^n/
               (n/2)! = C_n*Pi^floor(n/2)*r^n; sequence gives denominator of C_n.
%C A072346 Answer to question of how to extend the sequence 1, 2 r, Pi r^2, 4 Pi 
               r^3 / 3, Pi^2 r^4 / 2, ...
%C A072346 Surface area of n-dimensional sphere of radius r is n*V_n*r^(n-1).
%D A072346 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", 
               Springer-Verlag, p. 9, Eq. 17.
%H A072346 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Hypersphere.html">Hypersphere</a>
%H A072346 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Ball.html">Ball</a>
%H A072346 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Four-DimensionalGeometry.html">Four-Dimensional Geometry</a>
%F A072346 (n/2)! if n even, n!! if n odd.
%e A072346 Sequence of C_n's begins 1, 2, 1, 4/3, 1/2, 8/15, 1/6, 16/105, 1/24, 
               32/945, 1/120, 64/10395, ...
%t A072346 f[n_] := Pi^(n/2 - Floor[n/2])/(n/2)!; Table[ Denominator[ f[n]], {n, 
               0, 30} ]
%Y A072346 Cf. A072345.
%Y A072346 Cf. A001147.
%Y A072346 Sequence in context: A033314 A070260 A142705 this_sequence A103236 A141235 
               A051917
%Y A072346 Adjacent sequences: A072343 A072344 A072345 this_sequence A072347 A072348 
               A072349
%K A072346 nonn,frac
%O A072346 0,4
%A A072346 N. J. A. Sloane (njas(AT)research.att.com), Jul 31 2002

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