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

1,1

Links

Table of n, a(n) for n=1..87.

Wikipedia, Volume of an n-ball.

Formula

a(n) = round((Pi^(n/2)) / (Gamma(1 + n/2))).

Example

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.

Mathematica

Table[Round[(Pi^(n/2))/Gamma[1 + n/2]], {n, 120}] (* Michael De Vlieger, May 19 2016 *)

Prog

(PARI) a(n) = round((Pi^(n/2)) / (gamma(1+n/2)))

Crossrefs

Cf. A019699, A177677, A228272.

Sequence in context: A131845 A062186 A085763 * A281826 A062985 A168092

Adjacent sequences: A273261 A273262 A273263 * A273265 A273266 A273267

Keyword

nonn,easy

Author

Felix Fröhlich, May 18 2016

Status

approved