OFFSET
0,6
COMMENTS
The e.g.f. of x/2, tanh(cosec(x) - cot(x)) = x/(2^1*1!) - 8*x^5/(2^5*5!) - 112*x^7/(2^7*7!) - 128*x^9/(2^9*9!) + 109824*x^11/(2^11*11!) + ... is (up to signs) apparently provided by A003721.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..200
FORMULA
a(n) = numerator([x^(2*n+1)] tanh(tan(x/2))). - Peter Luschny, Nov 14 2016
EXAMPLE
Series starts: x/2 - x^5/480 - x^7/5760 - x^9/1451520 + 13*x^11/9676800 + 7951*x^13/49816166400 + ...
MAPLE
ser := series(tanh(tan(x/2)), x, 40):
seq(numer(coeff(ser, x, 2*n+1)), n=0..19); # Peter Luschny, Nov 14 2016
MATHEMATICA
Numerator[Take[CoefficientList[Series[Tanh[Csc[x] - Cot[x]], {x, 0, 40}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 12 2016 *)
CROSSREFS
KEYWORD
sign,frac
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
Name edited by R. J. Mathar, Dec 19 2011
STATUS
approved