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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 (list; graph; refs; listen; history; text; internal format)
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: A075602 A222985 A229833 * A172456 A022012 A022546

Adjacent sequences:  A305869 A305870 A305871 * A305873 A305874 A305875

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jun 12 2018

STATUS

approved

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Last modified June 21 18:42 EDT 2021. Contains 345365 sequences. (Running on oeis4.)