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%I #15 Apr 02 2021 10:41:38
%S 1,0,2,6,24,110,550,2922,16242,93520,553980,3359384,20777588,
%T 130696662,834244830,5393850898,35272830054,233016356788,
%U 1553427829684,10441803227652,70715551631992,482201548554776,3308810614160224,22836540660981088,158458108961055864
%N Number of friendly 3-watermelons of length n.
%D Essam, J.W. and Guttmann, A.J., 1995. Vicious walkers and directed polymer networks in general dimensions. Physical Review E, 52(6), pp. 5849ff. See (63).
%D Iwan Jensen, Three friendly walkers, Journal of Physics A: Mathematical and Theoretical, Volume 50:2 (2017), #24003, 14 pages; https://doi.org/10.1088/1751-8121/50/2/024003. See F_3(x).
%F G.f. = 1 - 2*x + G(x), where G(x) = 2*x+2*x^2+6*x^3+24*x^4+110*x^5+550*x^6+... is the g.f. for A342282.
%Y Cf. A001181, A342282.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Mar 19 2021
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