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 A013155 Expansion of e.g.f. exp(arctanh(x)+log(x+1)). 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 7 22:54 EDT 2024. Contains 375018 sequences. (Running on oeis4.)