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%I #12 Feb 26 2018 00:54:10
%S 1,3,9,34,121,468,1742,6802,25841,101428,389820,1535138,5944054,
%T 23461802,91314038,361034640,1410482689,5583955632,21878361324,
%U 86703276854,340483274100,1350453786234,5312965594054,21087370402596,83087565741142,329971068701702
%N Number of walks of length n on the square lattice that start from (0,0) and do not touch the nonpositive real axis once they have left their starting point.
%D Mireille Bousquet-Mélou and Gilles Schaeffer, Counting walks on the slit plane (extended abstract). Mathematics and computer science (Versailles, 2000), 101-112, Trends Math., Birkhäuser, Basel, 2000.
%H M. Bousquet-Mélou and Gilles Schaeffer, <a href="http://www.labri.fr/Perso/~bousquet/Articles/Slitplane/PTRF/final.ps.gz">Walks on the slit plane</a>, Probability Theory and Related Fields, Vol. 124, no. 3 (2002), 305-344.
%F G.f.: ((1+sqrt(1+4*t))^(1/2)*(1+sqrt(1-4*t))^(1/2))/(2*(1-4*t)^(3/4)).
%t CoefficientList[ Sqrt[(1+Sqrt[1-4*t])*(1+Sqrt[1+4*t])]/(2*(1-4*t)^(3/4))+O[t]^30, t] (* _Jean-François Alcover_, Jun 19 2015 *)
%Y Cf. A000108, A053792.
%K nonn
%O 0,2
%A _Mireille Bousquet-Mélou_, Mar 27 2000
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