A249700 Denominators of coefficients in series expansion of Cl_2(x)+x*log(x), where Cl_2 is the Clausen function of order 2.

1, 1, 1, 72, 1, 14400, 1, 1270080, 1, 87091200, 1, 5269017600, 1, 203997201408000, 1, 15692092416000, 1, 2902409413263360000, 1, 1747310222272462848000, 1, 337200218333282304000000, 1, 7135156619932253552640000, 1, 1016294482039046201671680000000

Offset

0,4

Links

Table of n, a(n) for n=0..25.

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

Cf. A027641, A027642, A249699.

Sequence in context: A373705 A036186 A036206 * A036178 A036187 A347918

Adjacent sequences: A249697 A249698 A249699 * A249701 A249702 A249703

Keyword

nonn,frac

Author

Jean-François Alcover, Nov 04 2014

Status

approved