A012383 arctanh(tan(x)*arcsin(x))=2/2!*x^2+12/4!*x^4+430/6!*x^6+26040/8!*x^8...

0, 2, 12, 430, 26040, 2903098, 482065540, 114403718182, 36427784932336, 15033693897929202, 7796959901543040892, 4965936966951067746846, 3810003526358223726689960, 3466033186882425920541836586

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) ~ (2*n-1)! / r^(2*n), where r = 0.8121639902962354379596899348276590246... is the root of the equation tan(r)*arcsin(r) = 1. - Vaclav Kotesovec, Feb 05 2015

Mathematica

With[{nn=30}, Flatten[{0, Take[Rest[CoefficientList[Series[ArcTanh[Tan[x] ArcSin[ x]], {x, 0, nn}], x]Range[0, nn]!], {2, -1, 2}]}]] (* Harvey P. Dale, Nov 01 2011 *)

Crossrefs

Sequence in context: A220113 A015181 A012378 * A012751 A012428 A012786

Adjacent sequences: A012380 A012381 A012382 * A012384 A012385 A012386

Keyword

nonn

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Extensions

Prepended missing a(0)=0 from Vaclav Kotesovec, Feb 05 2015

Status

approved