cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A280841 #21 Jan 30 2017 14:05:12
%S A280841 1,1,1,1727,20652479,2059268143,24860948333867803,
%T A280841 145905074443586569379,4567419249415312673370820607,
%U A280841 1642142815363470261591271553081,4093745592094627817260334517735412136353665283
%N A280841 Numerator of Integral_{x>=0} Product_{k=1..n} Sinc(x/k) dx / Pi.
%C A280841 Let I(n) be defined by I(n) = Integral_{x>=0} Product_{k=1..n} Sinc(x/k) dx.
%C A280841 I(1) = I(2) = I(3) = Pi/2, however I(4) = Pi/2 - Pi/3456.
%H A280841 Robert G. Wilson v, <a href="/A280841/b280841.txt">Table of n, a(n) for n = 1..15</a>
%e A280841 I(4) = 1727*Pi/3456. So a(4) = 1727.
%e A280841 I(5) = 20652479*Pi/41472000. So a(5) = 20652479.
%e A280841 I(6) = 2059268143*Pi/4147200000. So a(6) = 2059268143.
%e A280841 I(7) = 24860948333867803*Pi/50185433088000000. So a(7) = 24860948333867803.
%t A280841 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 A280841 Cf. A068214, A068215, A280842 (denominators).
%K A280841 nonn,frac,more
%O A280841 1,4
%A A280841 _Seiichi Manyama_, Jan 08 2017
%E A280841 a(8)-a(11) from _Alois P. Heinz_, Jan 09 2017