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%I #14 Oct 16 2018 12:35:59
%S 12317877,792534015,26225260226,600398249550,10743797911132,
%T 160576594766588,2089035241981688,24325590127655531,
%U 258634264294653390,2548272396065512974,23532893106071038404,205518653220527665304,1709552077642556424368,13623964536133602210560,104522878918062035228512
%N a(n) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus 4.
%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.
%F G.f.: y*(y-1)^9*(225225*y^8 + 25467156*y^7 + 207300366*y^6 + 77853486*y^5 - 660073489*y^4 + 222312257*y^3 + 269246651*y^2 - 140048085*y + 10034310)/(y-2)^26, where y=A000108(x).
%t Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
%t 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 a[n_] := Q[n, 2, 4];
%t Table[a[n], {n, 9, 23}] (* _Jean-François Alcover_, Oct 16 2018 *)
%Y Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, this sequence, 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 Column 2 of A269924.
%Y Cf. A000108.
%K nonn
%O 9,1
%A _Gheorghe Coserea_, Jun 08 2017
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