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%I #5 Jan 20 2013 12:12:27
%S 1,1,1,3,5,1,12,28,16,2,55,165,152,47,4,273,1001,1265,658,136,9,1428,
%T 6188,9919,7315,2547,392,21,7752,38760,75208,71981,35975,9252,1130,51,
%U 43263,245157,558144,657356,431599,159701,32286,3262,127,246675,1562275
%N Table T(n,k) = number of skeleta of (3+1)-free posets with n clone sets and k tangles
%H M. Guay-Paquet, A. H. Morales, E. Rowland, <a href="http://arxiv.org/abs/1212.5356">Structure and enumeration of (3+1)-free posets (extended abstract)</a>, arXiv:1212.5356 [math.CO], 2012.
%F G.f.: S(x, y) is the unique power series solution of the equation S(x, y) = 1 + S(x, y)^2 * x / (1 + x) + S(x, y)^3 * y.
%e There are 28 skeleta of (3+1)-free posets with 1 clone set and 2 tangles.
%e Table begins
%e 1 1 3 12 55 273 ...
%e 1 5 28 165 1001 6188 ...
%e 1 16 152 1265 9919 75208 ...
%e 2 47 658 7315 71981 657356 ...
%e 4 136 2547 35975 431599 4660516 ...
%e 9 392 9252 159701 2277821 28589750 ...
%e ......................................
%Y Cf. A079145, A079146, A221492, A221493
%K nonn,easy,tabl
%O 0,4
%A _Mathieu Guay-Paquet_, Jan 18 2013