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

0,2

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A127294 A012924 A024485 * A303224 A007501 A369996

Adjacent sequences: A013152 A013153 A013154 * A013156 A013157 A013158

Keyword

nonn

Author

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

Extensions

Definition clarified by Harvey P. Dale, Oct 05 2021

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

Status

approved