Tangent Number

Author

Eric W. Weisstein
January 16, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/TangentNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TangentNumber.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Series

Series[Tan[x],{x,0,10}]

Sum[(((((-1))^(n-1))(2^(2n))((2^(2n))-1)BernoulliB[2n])/((2n)!))(x^(2n-1)),{n,0,5}]

{1,2,16,272,7936}Table[((x^(2k-1))/((2k-1)!)),{k,5}]

Generalized

d[a_,n_]:=(2n-1)!((DirichletL[-a,2n+1])/(Sqrt[a]))(((((2a)/π)))^(2n))