A074454 Consider volume of unit sphere as a function of the dimension d; maximize this as a function of d (considered as a continuous variable); sequence gives decimal expansion of the resulting volume.

5, 2, 7, 7, 7, 6, 8, 0, 2, 1, 1, 1, 3, 4, 0, 0, 9, 9, 7, 2, 8, 2, 1, 4, 5, 8, 6, 4, 1, 7, 2, 8, 4, 6, 3, 8, 7, 5, 2, 9, 9, 9, 9, 2, 8, 4, 5, 1, 0, 1, 7, 3, 5, 6, 7, 7, 6, 1, 6, 3, 7, 3, 4, 0, 2, 1, 4, 8, 6, 4, 1, 2, 7, 3, 0, 5, 4, 7, 0, 1, 7, 1, 1, 0, 0, 6, 2, 0, 4, 8, 4, 0, 7, 2, 5, 8, 4, 0, 1

Offset

1,1

Comments

The dimension is given in A074455.

If you set v(n) = Pi^(n/2)/(n/2)! and s(n) = n*Pi^(n/2)/(n/2)! and then plot {6.283*v(n-2), s(n)} for 0<=n<=20, the two curves are almost identical.

Links

Table of n, a(n) for n=1..99.

Example

5.277768021113400997282145864172846387529999284510173567761637340214864\
12730547017110062048407258401284645...

Mathematica

d = x /. FindRoot[ PolyGamma[1 + x/2] == Log[Pi], {x, 5}, WorkingPrecision -> 105]; First[ RealDigits[ Pi^(d/2)/(d/2)!]][[1 ;; 99]] (* Jean-François Alcover, Apr 12 2013 *)

Crossrefs

Cf. A072345 & A072346.

Sequence in context: A364521 A253545 A195343 * A256110 A267211 A201423

Adjacent sequences: A074451 A074452 A074453 * A074455 A074456 A074457

Keyword

cons,nonn

Author

Robert G. Wilson v, Aug 22 2002

Extensions

Checked by Martin Fuller, Jul 12 2007

Status

approved