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%I #36 Apr 05 2024 11:10:14
%S 1,1,1,1,1,1,1,467807924713440738696537864469,
%T 17708695183056190642497315530628422295569865119,
%U 8096799621940897567828686854312535486311061114550605367511653,2051563935160591194337436768610392837217226815379395891838337765936509
%N Numerator of Borwein integral of order 2n+1.
%C From _Bill Gosper_, Jan 07 2009: (Start)
%C The numerator of (2/Pi)*Integrate[Product[Sinc[x/k], {k, 1, 2*n - 1, 2}], {x, 0, Infinity}]: Using Mathematica 7.0, we have:
%C In[6]:= Table[2/Pi*Integrate[Product[Sinc[x/k], {k, 1, 2*n - 1, 2}], {x, 0, Infinity}], {n, 8}]
%C Out[6]= {1, 1, 1, 1, 1, 1, 1, 467807924713440738696537864469/467807924720320453655260875000 }.
%C The denominators of this sequence are given in A144616.
%C The last term is 1 - 491^7 / (2^3 3^12 5^6 7^7 11^6 13^6). (End)
%H Robert G. Wilson v, <a href="/A068214/b068214.txt">Table of n, a(n) for n = 0..12</a>
%H J. M. Borwein, <a href="http://carmamaths.org/resources/jon/hhm.pdf">The Life of Modern Homo Habilis Mathematicus: Experimental Computation and Visual Theorems</a>, 2014; Chapter prepared for John Monaghan, Luc Troche and Jonathan Borwein, "Tools and mathematics: Instruments for learning", Spring-Verlag, 2015.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BorweinIntegrals.html">Borwein Integrals</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Borwein_integral">Borwein integral</a> (From _N. J. A. Sloane_, Feb 25 2012)
%t i[n_] := Times@@(Sin[x/# ]&/@Range[1, n, 2])/x^((n+1)/2)/Pi; Numerator[Table[Integrate[i[n], {x, 0, Infinity}], {n, 1, 19, 2}]]
%Y Cf. A068215, A144616.
%K nonn,frac,changed
%O 0,8
%A _Eric W. Weisstein_, Feb 21 2002
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