OFFSET
0,2
FORMULA
a(n) = (2*n+1)! * [x^(2*n+1)] arcsinh(x*sec(x)).
EXAMPLE
arcsinh(x*sec(x)) = x/1! + 2*x^3/3! + 4*x^5/5! - 8*x^7/7! + 2448*x^9/9! + ...
MATHEMATICA
nmax = 17; Table[(CoefficientList[Series[ArcSinh[x Sec[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
PROG
(PARI) first(n) = x='x+O('x^(2*n)); vecextract(Vec(serlaplace(asinh(x/cos(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 19 2017
STATUS
approved