A283103 - OEIS

%I #11 Feb 28 2017 22:45:18

%S 0,0,0,4,1380,75600,2340744,54275296,1055436228,18230184752,

%T 289150871152,4300858168200,60843411796440

%N Number of A'Campo forests of degree n and co-dimension 5.

%C a(n) is the number of A'Campo forests of degree n and of co-dimension 5.

%D P. Flajolet and 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}'(5,n)x^{5}y^{n} and N_{1}'(5,n) is the number of A'Campo forests with co-dimension 5; N_{2}(x,y)=\sum_{n}N_{2}'(5,n)x^{5}y^{n} where N_{2}'(5,n) is the number of partial configurations.

%e For n<4, the number of A'Campo forests of degree n  and co-dimension 5 is zero.

%e For n = 4 the number of A'Campo forests of co-dimension 5 is 4.

%Y Cf. A283101, A283102, A283049, A277877.

%K nonn

%O 1,4

%A _Noemie Combe_, Feb 28 2017

%E Added crossrefs