%I
%S 0,0,0,80,4845,138792,2893338,50507680,787265325,11345154600,
%T 154362306956,2010147294672,25288375607950
%N Number of A'Campo forests of degree n and codimension 4.
%C We can prove this using generating functions.
%D P. Flajolet R. Sedgewick, Analytic Combinatorics, Cambridge University Press (2009)
%H N. Combe, V. JugĂ©, <a href="https://arxiv.org/abs/1702.07672">Counting bicolored 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 (1N_{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}'(4,n)x^{4}y^{n} and N_{1}'(4,n) is the number of A'Campo forests with codimension 4; N_{2}(x,y)=\sum_{n}N_{2}'(4,n)x^{4}y^{n} where N_{2}'(4,n) is the number of partial configurations.
%e For n=1, n=2 and n=3, the number of A'Campo forests of codimension 4 is zero.
%e For n=4 the number of A'Campo forests of codimension 4 is 80.
%Y Cf. A283049, A277877, A283101, A283102, A283103.
%K nonn,more
%O 1,4
%A _Noemie Combe_, Feb 28 2017
