OFFSET
0,2
FORMULA
a(n) = (2*n+1)! * [x^(2*n+1)] arcsin(x*cosh(x)).
EXAMPLE
arcsin(x*cosh(x)) = x/1! + 4*x^3/3! + 44*x^5/5! + 1912*x^7/7! + 156816*x^9/9! + ...
MATHEMATICA
nmax = 15; Table[(CoefficientList[Series[ArcSin[x Cosh[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(asin(x*cosh(x)))), (4^n - 1)/3) \\ Iain Fox, Dec 19 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 19 2017
STATUS
approved