A012584 exp(arcsinh(x)*exp(x))=1+x+3/2!*x^2+9/3!*x^3+33/4!*x^4+145/5!*x^5...

1, 1, 3, 9, 33, 145, 715, 3801, 21889, 140001, 974803, 6947017, 50720417, 421135793, 3950147227, 33562929817, 240061039105, 2672302901185, 45695167547043, 388308372326665, -1858226878271967, 9709607588675537

Offset: 0

Author

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

Keywords

• sign

Programs

Mathematica

CoefficientList[Series[Exp[ArcSinh[x]*Exp[x]], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 31 2013 *)

Formula

E.g.f.: (x+sqrt(1+x^2))^(exp(x)). - Vaclav Kotesovec, Oct 31 2013

a(n) ~ 2*sin(n*Pi/2-1-Pi*cos(1)/2) * exp(-Pi*sin(1)/2) * n^(n-1) / exp(n). - Vaclav Kotesovec, Oct 31 2013