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A068215 Denominator of Borwein integral of order 2n+1, as defined by Weisstein.

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%I A068215 #26 Feb 16 2025 08:32:45
%S A068215 2,6,30,210,1890,20790,270270,1896516717212415135141110350293750000,
%T A068215 1220462921565155916674902677397230198502690752000000000
%N A068215 Denominator of Borwein integral of order 2n+1, as defined by Weisstein.
%H A068215 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BorweinIntegrals.html">Borwein Integrals</a>
%H A068215 Wikipedia, <a href="https://en.wikipedia.org/wiki/Borwein_integral">Borwein integral</a> [From _N. J. A. Sloane_, Feb 25 2012]
%F A068215 a(n) = A144616(n+1)*A097801(n+1) [assuming that the numerators are really A068214]. - _Andrey Zabolotskiy_, Oct 18 2016
%t A068215 i[n_] := Times@@(Sin[x/# ]&/@Range[1, n, 2])/x^((n+1)/2)/Pi; Denominator[Table[Integrate[i[n], {x, 0, \[Infinity]}], {n, 1, 19, 2}]]
%Y A068215 Cf. A068214 (supposed numerators), A144616 (denominators of the conventional Borwein integrals).
%K A068215 nonn,frac
%O A068215 0,1
%A A068215 _Eric W. Weisstein_, Feb 21 2002
%E A068215 Name edited by _Andrey Zabolotskiy_, Dec 14 2024