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A305872
Number of nonseparable rooted maps of genus n with one vertex and one face.
1
1, 1, 17, 1259, 200589, 54766516, 22839203295, 13532959408258, 10826939105517381, 11256605684271733244, 14762470788227855508388, 23845795018908512860754771, 46527914721396710095597849515, 107904469663880176355586920421756, 293401777662120053352713701982623322
OFFSET
0,3
LINKS
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
KEYWORD
nonn
AUTHOR
R. J. Mathar, Jun 12 2018
STATUS
approved