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

2, 6, 30, 210, 1890, 20790, 270270, 1896516717212415135141110350293750000, 1220462921565155916674902677397230198502690752000000000

Offset: 0

Author

Eric W. Weisstein, Feb 21 2002

Keywords

• nonn
• frac

Links

• Eric Weisstein's World of Mathematics, Borwein Integrals
• Wikipedia, Borwein integral [From _N. J. A. Sloane_, Feb 25 2012]

Crossrefs

Cf. A068214 (supposed numerators), A144616 (denominators of the conventional Borwein integrals).

Programs

Mathematica

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}]]

Formula

a(n) = A144616(n+1)*A097801(n+1) [assuming that the numerators are really A068214]. - Andrey Zabolotskiy, Oct 18 2016

Extensions

Name edited by Andrey Zabolotskiy, Dec 14 2024