A013155 Expansion of e.g.f. exp(arctanh(x)+log(x+1)).

1, 2, 3, 6, 21, 90, 495, 3150, 23625, 198450, 1885275, 19646550, 225935325, 2809456650, 37927664775, 547844046750, 8491582724625, 139700231921250, 2444754058621875, 45123174910563750, 879901910755993125, 18004146789314936250, 387089155970271129375, 8696002899239114208750

Offset: 0

Author

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

Keywords

• nonn

Examples

			G.f.= 1+2*x+3/2!*x^2+6/3!*x^3+21/4!*x^4+90/5!*x^5...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

a(2n+1) = 2 * A079484(n+1).

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Exp[ArcTanh[x]+Log[x+1]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 05 2021 *)

PARI

my(x='x+O('x^25)); Vec(serlaplace(exp(atanh(x)+log(x+1)))) \\ Christian Krause, Jan 05 2024

Formula

a(n) = 2*a(n-1) + ((2-n)^2-1)*a(n-2). - Christian Krause, Jan 05 2024

Extensions

Definition clarified by Harvey P. Dale, Oct 05 2021

Terms a(21) and beyond from Andrew Howroyd, Jan 05 2024