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

0,3

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.

Formula

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

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:

Prog

(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

Crossrefs

Cf. A035319.

Sequence in context: A222985 A229833 A362711 * A172456 A022012 A347851

Adjacent sequences: A305869 A305870 A305871 * A305873 A305874 A305875

Keyword

nonn

Author

R. J. Mathar, Jun 12 2018

Status

approved