Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (for n>3 the values are only conjectural).
Reference: J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xx.
The A-numbers refer to the decimal expansion of the corresponding constant in the OEIS.
N. J. A. Sloane, Feb. 10 2013

dim.      center-density            A-number           density                   A-number
      exact          decimal                 exact                 decimal
1     1/2            0.5000000000   -        1                     1             -
2     1/sqrt(12)     0.2886751347   A020769  (1/6)*3^(1/2)*Pi      0.9068996827  A093766
3     1/sqrt(32)     0.1767766952   A020789  (1/6)*2^(1/2)*Pi      0.7404804898  A093825
4     1/8            0.1250000000   -        (1/16)*Pi^2           0.6168502752  A222068
5     1/(8*sqrt(2))  0.08838834762  A222066  (1/30)*2^(1/2)*Pi^2   0.4652576133  A222069
6     1/(8*sqrt(3))  0.07216878367  A222067  (1/144)*3^(1/2)*Pi^3  0.3729475457  A222070
7     1/16           0.06250000000  -        (1/105)*Pi^3          0.2952978732  A222071
8     1/16           0.06250000000  -        (1/384)*Pi^4          0.2536695081  A222072
12    1/27           0.03703703704  -        (32/25515)*Pi^4       0.1221669964  A222073
16    1/16           0.06250000000  -        (1/1920)*Pi^5         0.1593852526  A222074
24    1              1              -        (64/10395)*Pi^5       1.884103881   A222075