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COMMENTS
| 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:
In[6]:= Table[2/Pi*Integrate[Product[Sinc[x/k], {k, 1, 2*n - 1, 2}], {x, 0, Infinity}], {n, 8}]
Out[6]= {1, 1, 1, 1, 1, 1, 1, 467807924713440738696537864469/467807924720320453655260875000 }. The denominators of this sequence are given in A144616.
The last term is 1 - 491^7 / (2^3 3^12 5^6 7^7 11^6 13^6). (End)
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MATHEMATICA
| 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}]]
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