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%I #20 Jan 30 2017 14:05:58
%S 2,2,2,3456,41472000,4147200000,50185433088000000,
%T 295090346557440000000,9251918060437194670080000000,
%U 3330690501757390081228800000000,8312243866372850396258184884618526720000000000
%N Denominator of Integral_{x>=0} Product_{k=1..n} Sinc(x/k) dx / Pi.
%C Let I(n) be defined by I(n) = Integral_{x>=0} Product_{k=1..n} Sinc(x/k) dx. I(1) = I(2) = I(3) = Pi/2, however I(4) = Pi/2 - Pi/3456.
%H Robert G. Wilson v, <a href="/A280842/b280842.txt">Table of n, a(n) for n = 1..15</a>
%e I(4) = 1727*Pi/3456. So a(4) = 3456.
%e I(5) = 20652479*Pi/41472000. So a(5) = 41472000.
%e I(6) = 2059268143*Pi/4147200000. So a(6) = 4147200000.
%e I(7) = 24860948333867803*Pi/50185433088000000. So a(7) = 50185433088000000.
%t f[n_] := Denominator[Integrate[Product[Sinc[x/k], {k, n}], {x, 0, Infinity}]/Pi]; Array[f, 11] (* _Robert G. Wilson v_, Jan 29 2017 *)
%Y Cf. A068214, A068215, A280841 (numerators).
%K nonn,frac,more
%O 1,1
%A _Seiichi Manyama_, Jan 08 2017
%E a(8)-a(11) from _Alois P. Heinz_, Jan 10 2017
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