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A288075 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 3.

%I A288075 #18 Jun 13 2017 12:18:58
%S A288075 1485,56628,1169740,17454580,211083730,2198596400,20465052608,
%T A288075 174437377400,1384928666550,10369994005800,73920866362200,
%U A288075 505297829133240,3331309741059300,21280393666593600,132216351453357600,801482122777393200,4752780295205269470,27632111202537355800
%N A288075 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 3.
%H A288075 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 A288075 A000108ser[n_] := (1 - Sqrt[1 - 4*x])/(2*x) + O[x]^(n+1);
%t A288075 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 A288075 Drop[CoefficientList[A288075ser[20], x], 6] (* _Jean-François Alcover_, Jun 13 2017, translated from PARI *)
%o A288075 (PARI)
%o A288075 A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
%o A288075 A288075_ser(N) = {
%o A288075   my(y = A000108_ser(N+1));
%o A288075   -11*y*(y-1)^6*(135*y^4 + 558*y^3 - 400*y^2 - 316*y + 158)/(y-2)^17;
%o A288075 };
%o A288075 Vec(A288075_ser(18))
%Y A288075 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 A288075 Column 1 of A269923, column 3 of A035309.
%Y A288075 Cf. A000108.
%K A288075 nonn
%O A288075 6,1
%A A288075 _Gheorghe Coserea_, Jun 07 2017