OFFSET
1,3
COMMENTS
LINKS
S.-J. Chern and J.D. Vaaler, The distribution of values of Mahler's measure, J. Reine. Angew. Math., 540 (2001), 1-47.
R, Grizzard and J. Gunther, Slicing the stars: counting algebraic numbers, integers, and units by degree and height, arXiv:1609.08720 [math.NT] 2016.
FORMULA
EXAMPLE
Fractions begin: 2, 4, 16/3, 64/9, 1024/135, 16384/2025, 524288/70875, 16777216/2480625, 4294967296/781396875, 1099511627776/246140015625, ....
MATHEMATICA
vol[d_] := (e = Floor[(d - 1)/2]; 2^(d - e) (e!)^-1 Product[(2 j/(2 j + 1))^(d - 2 j), {j, 1, e}] Sum[(-1)^j (d - 2 j)^e Binomial[e, j], {j, 0, e}]); Table[ Denominator[ vol[d]], {d, 1, 17}]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jonathan Sondow, Jun 15 2017
STATUS
approved