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%I #21 May 10 2020 02:59:35
%S 1,2,4,11,40,185,1030,6785,51160,438425,4176250,44098925,507867100,
%T 6375156125,86130937750,1253044612625,19429666282000,321457635604625,
%U 5626346310003250,104323833636303125,2034312191276462500
%N Expansion of e.g.f.: exp(arctanh(x)+arcsin(x)).
%H Vincenzo Librandi, <a href="/A013170/b013170.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = n * A006228(n) + A006228(n+1). - _Mark van Hoeij_, Aug 27 2005
%F a(n) = (n^2-3*n+5)*a(n-2) + (n^2-6*n+10)*a(n-3). - _Vaclav Kotesovec_, Oct 07 2012
%e exp(arctanh(x)+arcsin(x)) = 1+2*x+4/2!*x^2+11/3!*x^3+40/4!*x^4+185/5!*x^5+...
%t Table[n!*SeriesCoefficient[E^(ArcTanh[x]+ArcSin[x]),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 07 2012 *)
%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(atanh(x)+asin(x)))) \\ _Joerg Arndt_, May 04 2013
%Y Cf. A006228.
%K nonn
%O 0,2
%A Patrick Demichel (patrick.demichel(AT)hp.com)
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