OFFSET
0,4
LINKS
Eric Weisstein's MathWorld, Clausen Function
Eric Weisstein's MathWorld, Clausen's Integral
FORMULA
Denominators of BernoulliB(n - 1)/((n - 1)*n!), except the first 3 terms.
EXAMPLE
Coefficients begin 0, 1, 0, 1/72, 0, 1/14400, 0, 1/1270080, 0, 1/87091200, 0, 1/5269017600, 0, 691/203997201408000, ...
MATHEMATICA
Clausen2[x_] := (I/2)*(PolyLog[2, Exp[-I*x]] - PolyLog[2, Exp[I*x]]); a[n_] := SeriesCoefficient[Clausen2[x] + x*Log[x], {x, 0, n}]; (* or *) a[n_] := If[Mod[n, 4] == 3, 1, -1]*BernoulliB[n - 1]/((n - 1)*n!); a[0] = a[2] = 0; a[1] = 1; Table[a[n] // Denominator, {n, 0, 30}] (* Apparently this only works with an older version of Mma *)
Flatten[{1, 1, Table[If[EvenQ[n], Denominator[Zeta[n]/(n*(n+1)*2^(n-1)*Pi^n)], 1], {n, 1, 20}]}] (* Vaclav Kotesovec, Nov 04 2014 *)
PROG
(Magma) [1, 1, 1] cat [Denominator(Bernoulli(n - 1)/((n - 1)*Factorial(n))) : n in [3..50]]; // Vincenzo Librandi, Nov 05 2014
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jean-François Alcover, Nov 04 2014
STATUS
approved