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A273264
Volume of unit n-ball, rounded to the nearest integer.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Felix Fröhlich, May 18 2016
STATUS
approved