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%I #13 Feb 28 2017 22:42:45
%S 0,0,4,344,8760,157504,2388204,32737984,419969088,5141235840,
%T 60795581132,700024311536,7892352548080
%N Numbers of A'Campo forests of degree n>2 and co-dimension 3.
%C We can prove this using generating functions.
%D P. Flajolet R. Sedgewick, Analytic Combinatorics, Cambridge University Press (2009)
%H N. Combe, V. Jugé, <a href="http://arxiv.org/abs/1702.07672">Counting bi-colored A'Campo forests</a>, arXiv:1702.07672 [Math.AG], 2017.
%F a(n) is obtained by using the generating function N_{1} =1+yN_{2}^4 and (1-N_{2} +2yN_{2}^4 -yN_{2}^{5} +xyN_{2}^{6} +y^{2}N_{2}^{8})(1+yN_{2}^{4}-xyN_{2}^{5})+x^3y^{2}N_{2}^{9} =0, where N_{1}(x,y)=\sum_{n}N_{1}'(3,n)x^{3}y^{n} and N_{1}'(3,n) is the number of A'Campo forests with co-dimension 3; N_{3}(x,y)=\sum_{n}N_{3}'(3,n)x^{3}y^{n} where N_{3}'(3,n) is the number of partial configurations.
%e For n=3, there exist four A'Campo forests of co-dimension 3 and degree 3.
%e For n=2 there do not exist any A'Campo forests of co-dimension 3.
%K nonn
%O 1,3
%A _Noemie Combe_, Feb 28 2017
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