|
%I #16 Jun 14 2018 06:36:09
%S 1,1,17,1259,200589,54766516,22839203295,13532959408258,
%T 10826939105517381,11256605684271733244,14762470788227855508388,
%U 23845795018908512860754771,46527914721396710095597849515,107904469663880176355586920421756,293401777662120053352713701982623322
%N Number of nonseparable rooted maps of genus n with one vertex and one face.
%H Gheorghe Coserea, <a href="/A305872/b305872.txt">Table of n, a(n) for n = 0..200</a>
%H T. R. S. Walsh, A. B. Lehman, <a href="https://dx.doi.org/10.1016/0095-8956(75)90050-7">Counting rooted maps by genus. III: Nonseparable maps</a>, J. Combinatorial Theory Ser. B 18 (1975), 222-259.
%F The g.f. A(x) satisfies A035319(x) = A[x*(A035319(x)^4)], where A035319 is the o.g.f. of A035319.
%p g := 1+x ;
%p for itr from 2 to 14 do
%p g := g+a*x^itr;
%p Ax := add(A035319(i)*x^i,i=0..itr+1) ;
%p x*Ax^4 ;
%p z := subs(x=%,g)-Ax ;
%p z := expand(z) ;
%p z := taylor(z,x=0,itr+1) ;
%p z := convert(z,polynom) ;
%p aa := solve(z,a) ;
%p g := g-a*x^itr+aa*x^itr ;
%p print(g) ;
%p end do:
%o (PARI)
%o seq(N) = {
%o my(s = 1+'x*Ser(vector(N, n, (4*n)!/((2*n+1)!*4^n))));
%o Vec(subst(s, 'x, serreverse('x*s^4)));
%o };
%o seq(14) \\ _Gheorghe Coserea_, Jun 13 2018
%Y Cf. A035319.
%K nonn
%O 0,3
%A _R. J. Mathar_, Jun 12 2018
| 