A013069 Expansion of e.g.f.: exp(arcsinh(x)+log(x+1))=1+2*x+3/2!*x^2+3/3!*x^3-3/4!*x^4-15/5!*x^5...

1, 2, 3, 3, -3, -15, 45, 315, -1575, -14175, 99225, 1091475, -9823275, -127702575, 1404728325, 21070924875, -273922023375, -4656674397375, 69850115960625, 1327152203251875, -22561587455281875

Offset: 0

Author

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

Keywords

• sign

Crossrefs

Cf. A046126.

a(2n) = (-1)^(n+1) * A079484(n), n>1.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[ArcSinh[x]+Log[x+1]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 15 2024 *)

Extensions

Definition clarified by Harvey P. Dale, Aug 15 2024