OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..200
FORMULA
a(n) = (2*n)! * [x^(2*n)] log(1 + x*tanh(x/2)).
a(n) ~ -(-1)^n * sqrt(Pi) * 2^(2*n + 1) * n^(2*n - 1/2) / (r^(2*n) * exp(2*n)), where r = 1.306542374188806202228727831923118284841279755635... is the root of the equation r * tan(r/2) = 1. - Vaclav Kotesovec, Dec 21 2017
EXAMPLE
log(1 + x*tanh(x/2)) = x^2/2! - 4*x^4/4! + 48*x^6/6! - 1186*x^8/8! + ...
MATHEMATICA
nmax = 16; Table[(CoefficientList[Series[Log[1 + x Tanh[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 21 2017
STATUS
approved