OFFSET
0,3
FORMULA
a(n) = (2n)! * [x^(2n)] -arcsin(log(x+1)-arctanh(x)).
a(n) ~ 2^(2*n) * n^(2*n-1) / (1/(exp(1)-sqrt(exp(2)-1)) - exp(1))^(2*n-1). - Vaclav Kotesovec, Jan 02 2014
EXAMPLE
+arcsin(log(x+1)-arctanh(x)) = 0 -1/2!*x^2 -6/4!*x^4 -135/6!*x^6 -6300/8!*x^8...
MATHEMATICA
With[{nn=40}, Take[CoefficientList[Series[-ArcSin[Log[x+1]-ArcTanh[x]], {x, 0, nn}], x] Range[0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jul 22 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Patrick Demichel (patrick.demichel(AT)hp.com)
EXTENSIONS
Zero prepended by and more terms from Harvey P. Dale, Jul 22 2013
STATUS
approved