A012251 exp(arcsinh(arctan(x)))=1+x+1/2!*x^2-2/3!*x^3-11/4!*x^4+24/5!*x^5...

1, 1, 1, -2, -11, 24, 349, -720, -22455, 40320, 2465241, -3628800, -416217603, 479001600, 100729124469, -87178291200, -33198564667887, 20922789888000, 14328891118054449, -6402373705728000, -7852649782447649403

Offset: 0

Author

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

Keywords

• sign

Crossrefs

Bisections are (-1)^n*A010050 and (-1)^n*A012138.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[ArcSinh[ArcTan[x]]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 26 2011 *)

Formula

E.g.f.: Q(0)-1, where Q(k) = 2 + arctan(x)/(1 - arctan(x)/Q(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 19 2013