A225123 Denominators of Integral_{x=0..Pi/2} sin(2*n*x)*log(cosec(x)) dx.

1, 2, 2, 18, 3, 150, 90, 1470, 105, 5670, 3150, 76230, 10395, 1171170, 630630, 1351350, 45045, 26036010, 13783770, 552882330, 72747675, 87297210, 320089770, 15393408030, 1003917915, 83659826250, 43503109650, 271057837050, 35137127025, 8442949665150, 4367042930250

Offset

0,2

References

George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), p. 218.

Links

Table of n, a(n) for n=0..30.

Example

0, 1/2, 1/2, 7/18, 1/3, 43/150, 23/90, 337/1470, 22/105, 1091/5670, 563/3150, ... = A225122/A225123

Maple

a:= n-> denom(Re(int(sin(2*n*x)*log(csc(x)), x=0..Pi/2))):
seq(a(n), n=0..30);  # Alois P. Heinz, Apr 29 2013

Mathematica

a[n_] := Integrate[Sin[2*n*x]*Log[Csc[x]], {x, 0, Pi/2}]; Table[a[n] // Denominator, {n, 0, 30}]

Crossrefs

Cf. A225122 (numerators).

Sequence in context: A297794 A291765 A231123 * A087338 A055735 A168296

Adjacent sequences: A225120 A225121 A225122 * A225124 A225125 A225126

Keyword

nonn,easy,frac

Author

Jean-François Alcover, Apr 29 2013

Status

approved