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%I #5 Jul 30 2020 14:40:07
%S 7,40,125,260,409,513,537,482,379,265,167,95,50,25,11,5,2,1,1,1,1,1,1,
%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N Ceiling of 2^(n-1) times the surface area of the unit sphere in 2n-dimensional space.
%C The rounded values of this real sequence is A164082, the floor is A164081.
%C The surface area of n-dimensional sphere of radius r is n*V_n*r^(n-1); see A072478/A072479.
%D Conway, J. H. and Sloane, N. J. A. Sphere Packings, Lattices, and Groups, 2nd ed. New York: Springer-Verlag, p. 9, 1993.
%D Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973.
%D Sommerville, D. M. Y. An Introduction to the Geometry of n Dimensions. New York: Dover, p. 136, 1958.
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/Hypersphere.html">Hypersphere</a>,
%F a(n) = ceiling(((2*pi)^n)/(n-1)!).
%e Table of approximate real values before rounding up.
%e ========================
%e n ((2*pi)^n) / (n-1)!
%e 1 6.28318531 = A019692
%e 2 39.4784176 = 2*A164102
%e 3 124.025107 = 4*A091925
%e 4 259.757576 = 8*A164109
%e 5 408.026246
%e 6 512.740903
%e 7 536.941018
%e 8 481.957131
%e 9 378.528246
%e 10 264.262568
%e 11 166.041068
%e 12 94.8424365
%e 13 49.6593836
%e 14 24.00147
%e 15 10.7718345
%e 16 4.5120955
%e 17 1.77189576
%e 18 0.654891141
%e 19 0.228600133
%e 20 0.075596684
%e ========================
%t Table[Ceiling[(2Pi)^n/(n-1)!],{n,60}] (* _Harvey P. Dale_, Jul 30 2020 *)
%Y Cf. A072345, A072346, A072478, A072479, A074457, A122510, A154255, A164081, A164082.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Aug 09 2009
%E Definition corrected - _R. J. Mathar_, Sep 09 2009
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