A273264 Volume of unit n-ball, rounded to the nearest integer.
2, 3, 4, 5, 5, 5, 5, 4, 3, 3, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1
Examples
The volume of the unit 3-ball (the set of points of distance equal to or less than the radius of the midpoint of the ordinary sphere or 2-sphere) is equal to 4/3*Pi, which is 4.1887902047... (A019699) and when rounded down this is 4, so a(3) = 4.
Links
- Wikipedia, Volume of an n-ball.
Programs
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Mathematica
Table[Round[(Pi^(n/2))/Gamma[1 + n/2]], {n, 120}] (* Michael De Vlieger, May 19 2016 *) -
PARI
a(n) = round((Pi^(n/2)) / (gamma(1+n/2)))
Formula
a(n) = round((Pi^(n/2)) / (Gamma(1 + n/2))).