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A288271 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 4.

%I A288271 #17 Oct 16 2018 12:35:22
%S A288271 225225,12317877,351683046,7034538511,111159740692,1480593013900,
%T A288271 17302190625720,182231849209410,1763184571730010,15894791312284170,
%U A288271 134951136993773100,1088243826731751690,8391311316938069520,62210659883935683120,445441857820701181440,3092035882104030618900
%N A288271 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 4.
%H A288271 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.
%F A288271 G.f.: -143*y*(y-1)^8*(1575*y^6 + 13689*y^5 + 4689*y^4 - 34417*y^3 + 11361*y^2 + 7017*y - 2339)/(y-2)^23, where y=A000108(x).
%t A288271 Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
%t A288271 Q[n_, f_, g_] := Q[n, f, g] = 6/(n+1)((2n-1)/3 Q[n-1, f, g] + (2n-1)/3 Q[n - 1, f-1, g] + (2n-3)(2n-2)(2n-1)/12 Q[n-2, f, g-1] + 1/2 Sum[l = n-k; Sum[v = f-u; Sum[j = g-i; Boole[l >= 1 && v >= 1 && j >= 0] (2k-1)(2l-1) Q[k-1, u, i] Q[l-1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
%t A288271 a[n_] := Q[n, 1, 4];
%t A288271 Table[a[n], {n, 8, 23}] (* _Jean-François Alcover_, Oct 16 2018 *)
%o A288271 (PARI)
%o A288271 A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
%o A288271 A288271_ser(N) = {
%o A288271   my(y = A000108_ser(N+1));
%o A288271   -143*y*(y-1)^8*(1575*y^6 + 13689*y^5 + 4689*y^4 - 34417*y^3 + 11361*y^2 + 7017*y - 2339)/(y-2)^23;
%o A288271 };
%o A288271 Vec(A288271_ser(16))
%Y A288271 Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: this sequence, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.
%Y A288271 Column 1 of A269924.
%Y A288271 Cf. A000108.
%K A288271 nonn
%O A288271 8,1
%A A288271 _Gheorghe Coserea_, Jun 08 2017