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%I #12 Oct 17 2018 12:32:10
%S 158959754226,14805457339920,691650582088536,21853758736216200,
%T 528887751025584600,10499075716384241952,178505550201444784920,
%U 2677324515710001081372,36188783145801243558900,447964809766718459342400,5141788096308757330278816,55267879542927003057175200,560775739552815581754138816
%N a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 5.
%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.: -6*y*(y-1)^12*(1434672330*y^11 + 125297167569*y^10 + 1520299523980*y^9 + 3143130463894*y^8 - 7464422123238*y^7 - 7957464673806*y^6 + 16850577489362*y^5 - 2273292547090*y^4 - 6843677356968*y^3 + 3164962758706*y^2 - 181381616688*y - 58970465680)/(y-2)^35, 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) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 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] (2 k - 1) (2 l - 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, 3, 5];
%t Table[a[n], {n, 12, 24}] (* _Jean-François Alcover_, Oct 17 2018 *)
%Y Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, this sequence, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
%Y Column 3 of A269925.
%Y Cf. A000108.
%K nonn
%O 12,1
%A _Gheorghe Coserea_, Jun 09 2017
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