OFFSET
0,14
LINKS
Eric Weisstein's MathWorld, Clausen Function
Eric Weisstein's MathWorld, Clausen's Integral
FORMULA
Numerators 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, ...
MAPLE
A249699List := proc(len) local mu, ser;
mu := h -> sum(bernoulli(2*k)/(2*k)!*h^(2*k-1), k=0..infinity);
ser := series(mu(h), h, len+2): seq((-1)^binomial(n, 2)*numer(coeff(ser, h, n)), n=0..len): 0, 1, op([%]) end: A249699List(48); # Peter Luschny, Dec 05 2018
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] // Numerator, {n, 0, 30}] (* Apparently this only works with an older version of Mma *)
Flatten[{0, 1, Table[If[EvenQ[n], Numerator[Zeta[n]/(n*(n+1)*2^(n-1)*Pi^n)], 0], {n, 1, 30}]}] (* Vaclav Kotesovec, Nov 04 2014 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Jean-François Alcover, Nov 04 2014
EXTENSIONS
More terms from Peter Luschny, Dec 05 2018
STATUS
approved