|
%I #18 Jun 13 2017 12:18:58
%S 1485,56628,1169740,17454580,211083730,2198596400,20465052608,
%T 174437377400,1384928666550,10369994005800,73920866362200,
%U 505297829133240,3331309741059300,21280393666593600,132216351453357600,801482122777393200,4752780295205269470,27632111202537355800
%N a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 3.
%H Sean R. Carrell, Guillaume Chapuy, <a href="http://arxiv.org/abs/1402.6300">Simple recurrence formulas to count maps on orientable surfaces</a>, arXiv:1402.6300 [math.CO], 2014.
%t A000108ser[n_] := (1 - Sqrt[1 - 4*x])/(2*x) + O[x]^(n+1);
%t A288075ser[n_] := (y = A000108ser[n+1]; -11*y*(y-1)^6*(135*y^4 + 558*y^3 - 400*y^2 - 316*y + 158)/(y-2)^17);
%t Drop[CoefficientList[A288075ser[20], x], 6] (* _Jean-François Alcover_, Jun 13 2017, translated from PARI *)
%o (PARI)
%o A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
%o A288075_ser(N) = {
%o my(y = A000108_ser(N+1));
%o -11*y*(y-1)^6*(135*y^4 + 558*y^3 - 400*y^2 - 316*y + 158)/(y-2)^17;
%o };
%o Vec(A288075_ser(18))
%Y Rooted maps of genus 3 with n edges and f faces for 1<=f<=10: this sequence, A288076 f=2, A288077 f=3, A288078 f=4, A288079 f=5, A288080 f=6, A288081 f=7, A288262 f=8, A288263 f=9, A288264 f=10.
%Y Column 1 of A269923, column 3 of A035309.
%Y Cf. A000108.
%K nonn
%O 6,1
%A _Gheorghe Coserea_, Jun 07 2017
| 