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Number of A'Campo forests of degree n>1 and co-dimension 2.
3

%I #18 Feb 28 2017 02:47:03

%S 0,30,608,8740,109296,1269450,14096320,151927776,1603346160,

%T 16659866938,171064877280

%N Number of A'Campo forests of degree n>1 and co-dimension 2.

%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}'(2,n)x^{2}y^{n} and N_{1}'(2,n) is the number of A'Campo forests with co-dimension 2; N_{2}(x,y)=\sum_{n}N_{2}'(2,n)x^{2}y^{n} where N_{2}'(2,n) is the number of partial configurations.

%e For n=3 we have a(3)=30 A'Campo forests of co-dimension 2.

%K nonn,more

%O 1,2

%A _Noemie Combe_, Feb 27 2017