Search: id:A068214
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%I A068214
%S A068214 1,1,1,1,1,1,1,467807924713440738696537864469,
%T A068214 17708695183056190642497315530628422295569865119,
%U A068214 8096799621940897567828686854312535486311061114550605367511653
%N A068214 Numerator of Borwein integral of order 2n+1.
%C A068214 Comment from R. W. Gosper (rwg(AT)sdf.lonestar.org), Jan 07 2009: (Start) 
               Also 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 A068214 In[6]:= Table[2/Pi*Integrate[Product[Sinc[x/k], {k, 1, 2*n - 1, 2}], 
               {x, 0, Infinity}], {n, 8}]
%C A068214 Out[6]= {1, 1, 1, 1, 1, 1, 1, 467807924713440738696537864469/467807924720320453655260875000 
               }. The denominators of this sequence are given in A144616.
%C A068214 The last term is 1 - 491^7 / (2^3 3^12 5^6 7^7 11^6 13^6). (End)
%H A068214 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BorweinIntegrals.html">Borwein Integrals</a>
%t A068214 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 A068214 Cf. A068215, A144616.
%Y A068214 Sequence in context: A104300 A095450 A095452 this_sequence A144616 A095454 
               A058446
%Y A068214 Adjacent sequences: A068211 A068212 A068213 this_sequence A068215 A068216 
               A068217
%K A068214 nonn,frac
%O A068214 0,8
%A A068214 Eric Weisstein (eric(AT)weisstein.com), Feb 21, 2002

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