Sequence with floatingpoint numbers

[Max Alekseyev]

sven-h.simon wrote:
> I would like to contribute the following sequence, which I found 
> somehow interesting:
> 
> 3.14159265358979323846,4.18879020478639098461,4.93480220054467930941,
> 5.26378901391432459671,5.16771278004997002924,4.72476597033140116959,
> 4.05871212641676821818,3.29850890273870686938,2.55016403987734544385,
> 1.88410387938990024134,1.33526276885458949587,0.91062875478328314603,
> 0.59926452932079207688,0.38144328082330448281,0.23533063035889320454,
> 0.14098110691713903791,0.08214588661112822879,0.04662160103008854577,
> 0.02580689139001406001
> 
> It is the n-dimensional volume of a n-dimensional sphere with radius 1 for
> n = 2 to 20.

There is an explicit formula for that:

V_n = \pi^{n/2} / \Gamma(n/2 + 1)

In particular,

V_{2k} = \pi^k / k!

V_{2k+1} = \pi^k 2^{k+1} / (2k+1)!!

where (2k+1)!! = (2k+1)*(2k-1)*(2k-3)*...*1

Max