for odd .
The integrals are curious because the terms , 3, ..., 13 all have unit numerators,
but ,
17, ... do not. The sequence of values of for , 3, ... is given by 1/2, 1/6, 1/30, 1/210, 1/1890, 1/20790,
1/270270, 467807924713440738696537864469/1896516717212415135141110350293750000, ...
(OEIS A068214 and A068215;
Borwein et al. 2004, p. 98; Bailey et al. 2006).
Bailey, D. H.; Borwein, J. M.; Kapoor, V.; and Weisstein, E. W. "Ten Problems in Experimental Mathematics." Amer.
Math. Monthly113, 481-509, 2006.Borwein, D. and Borwein,
J. M. "Some Remarkable Properties of Sinc and Related Integrals."
Ramanujan J.5, 73-90, 2001.Borwein, D.; Borwein, J. M.;
and Mares, B. A. Jr. "Multi-Variable Sinc Integrals and Volumes of Polyhedra."
Preprint. 2001. http://www.cecm.sfu.ca/preprints/2001pp.html.Borwein,
J.; Bailey, D.; and Girgensohn, R. "Some Curious Sinc Integrals." §2.5
in Experimentation
in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters,
p. 98, 2004.Sloane, N. J. A. Sequences A068214
and A068215 in "The On-Line Encyclopedia
of Integer Sequences."
.
The integrals are curious because the terms 
, 3, ..., 13 all have unit numerators,
but 
,
17, ... do not. The sequence of values of 
for 
, 3, ... is given by 1/2, 1/6, 1/30, 1/210, 1/1890, 1/20790,
1/270270, 467807924713440738696537864469/1896516717212415135141110350293750000, ...
(OEIS A068214 and A068215;
Borwein et al. 2004, p. 98; Bailey et al. 2006).
