A305872 Number of nonseparable rooted maps of genus n with one vertex and one face.

1, 1, 17, 1259, 200589, 54766516, 22839203295, 13532959408258, 10826939105517381, 11256605684271733244, 14762470788227855508388, 23845795018908512860754771, 46527914721396710095597849515, 107904469663880176355586920421756, 293401777662120053352713701982623322

Offset: 0

Author

R. J. Mathar, Jun 12 2018

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 0..200
• T. R. S. Walsh, A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

Crossrefs

Cf. A035319.

Programs

Maple

g := 1+x ;
for itr from 2 to 14 do
    g := g+a*x^itr;
    Ax := add(A035319(i)*x^i,i=0..itr+1) ;
    x*Ax^4 ;
    z := subs(x=%,g)-Ax ;
    z := expand(z) ;
    z := taylor(z,x=0,itr+1) ;
    z := convert(z,polynom) ;
    aa := solve(z,a) ;
    g := g-a*x^itr+aa*x^itr ;
    print(g) ;
end do:

PARI

seq(N) = {
  my(s = 1+'x*Ser(vector(N, n, (4*n)!/((2*n+1)!*4^n))));
  Vec(subst(s, 'x, serreverse('x*s^4)));
};
seq(14) \\ Gheorghe Coserea, Jun 13 2018

Formula

The g.f. A(x) satisfies A035319(x) = A[x*(A035319(x)^4)], where A035319 is the o.g.f. of A035319.