

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.


2



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
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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(n2), 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]] (* JeanFrançois Alcover, Apr 12 2013 *)


CROSSREFS

Cf. A072345 & A072346.
Sequence in context: A204899 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



