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%I #18 Jan 05 2024 14:49:31
%S 1,2,3,6,21,90,495,3150,23625,198450,1885275,19646550,225935325,
%T 2809456650,37927664775,547844046750,8491582724625,139700231921250,
%U 2444754058621875,45123174910563750,879901910755993125,18004146789314936250,387089155970271129375,8696002899239114208750
%N Expansion of e.g.f. exp(arctanh(x)+log(x+1)).
%H Andrew Howroyd, <a href="/A013155/b013155.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = 2*a(n-1) + ((2-n)^2-1)*a(n-2). - _Christian Krause_, Jan 05 2024
%e G.f.= 1+2*x+3/2!*x^2+6/3!*x^3+21/4!*x^4+90/5!*x^5...
%t With[{nn=20},CoefficientList[Series[Exp[ArcTanh[x]+Log[x+1]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 05 2021 *)
%o (PARI) my(x='x+O('x^25)); Vec(serlaplace(exp(atanh(x)+log(x+1)))) \\ _Christian Krause_, Jan 05 2024
%Y a(2n+1) = 2 * A079484(n+1).
%K nonn
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
%E Definition clarified by _Harvey P. Dale_, Oct 05 2021
%E Terms a(21) and beyond from _Andrew Howroyd_, Jan 05 2024
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