A013295 E.g.f.: -arcsin(log(x+1)-arctanh(x)) (even powers only).

0, 1, 6, 135, 6300, 503685, 61434450, 10620124515, 2471073204600, 744907219281225, 282494651079390750, 131664032748125452575, 73997676994079578439700, 49364071776588936300058125, 38571353476865946088188086250, 34900798662291878654547561226875

Offset

0,3

Links

Table of n, a(n) for n=0..15.

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

Sequence in context: A241999 A333005 A013299 * A214132 A196703 A196852

Adjacent sequences: A013292 A013293 A013294 * A013296 A013297 A013298

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