A012709 exp(arctanh(x)*exp(x))=1+x+3/2!*x^2+12/3!*x^3+57/4!*x^4+340/5!*x^5...

1, 1, 3, 12, 57, 340, 2305, 18186, 158977, 1560840, 16695553, 196272142, 2483596577, 34036624700, 497515462561, 7792454528002, 129248702613505, 2278494692749840, 42291311707716609, 828953188249846678

Offset: 0

Author

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

Keywords

• nonn

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[ArcTanh[x]Exp[x]],{x,0,nn}], x]Range[0,nn]!] (* Harvey P. Dale, Jan 14 2012 *)

Formula

a(n) ~ (n-1)! * (2*n)^(exp(1)/2) / GAMMA(exp(1)/2). - Vaclav Kotesovec, Oct 24 2013