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%I #9 Apr 30 2013 12:17:41
%S 1,2,2,18,3,150,90,1470,105,5670,3150,76230,10395,1171170,630630,
%T 1351350,45045,26036010,13783770,552882330,72747675,87297210,
%U 320089770,15393408030,1003917915,83659826250,43503109650,271057837050,35137127025,8442949665150,4367042930250
%N Denominators of Integral_{x=0..Pi/2} sin(2*n*x)*log(cosec(x)) dx.
%D George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 218.
%e 0, 1/2, 1/2, 7/18, 1/3, 43/150, 23/90, 337/1470, 22/105, 1091/5670, 563/3150, ... = A225122/A225123
%p a:= n-> denom(Re(int(sin(2*n*x)*log(csc(x)), x=0..Pi/2))):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Apr 29 2013
%t a[n_] := Integrate[Sin[2*n*x]*Log[Csc[x]], {x, 0, Pi/2}]; Table[a[n] // Denominator, {n, 0, 30}]
%Y Cf. A225122 (numerators).
%K nonn,easy,frac
%O 0,2
%A _Jean-François Alcover_, Apr 29 2013
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