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A280841 Numerator of Integral_{x>=0} Product_{k=1..n} Sinc(x/k) dx / Pi. 2

%I

%S 1,1,1,1727,20652479,2059268143,24860948333867803,

%T 145905074443586569379,4567419249415312673370820607,

%U 1642142815363470261591271553081,4093745592094627817260334517735412136353665283

%N Numerator 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.

%C I(1) = I(2) = I(3) = Pi/2, however I(4) = Pi/2 - Pi/3456.

%H Robert G. Wilson v, <a href="/A280841/b280841.txt">Table of n, a(n) for n = 1..15</a>

%e I(4) = 1727*Pi/3456. So a(4) = 1727.

%e I(5) = 20652479*Pi/41472000. So a(5) = 20652479.

%e I(6) = 2059268143*Pi/4147200000. So a(6) = 2059268143.

%e I(7) = 24860948333867803*Pi/50185433088000000. So a(7) = 24860948333867803.

%t f[n_] := Numerator[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, A280842 (denominators).

%K nonn,frac,more

%O 1,4

%A _Seiichi Manyama_, Jan 08 2017

%E a(8)-a(11) from _Alois P. Heinz_, Jan 09 2017

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Last modified June 15 04:47 EDT 2021. Contains 345043 sequences. (Running on oeis4.)