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%I #14 Oct 16 2018 13:49:03
%S 1480593013900,160576594766588,8615949311310872,309197871098871838,
%T 8419549939292302908,186553519919803261860,3515647035511186627416,
%U 58089920897558352891672,860337164444236894357488,11612741439751867739074432,144715531380208437909370144,1682205432436689960841795876
%N a(n) is the number of rooted maps with n edges and 6 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.: 2*y*(y-1)^13*(1208305403982*y^12 + 42344287039512*y^11 + 283047148578040*y^10 + 47183718440672*y^9 - 1618438221531593*y^8 + 617910272368381*y^7 + 2488374601412831*y^6 - 2268379207704481*y^5 - 116197489174642*y^4 + 764144804102008*y^3 - 252877960850800*y^2 + 8651012216320*y + 3769026206720)/(y-2)^38, 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, 6, 4];
%t Table[a[n], {n, 13, 24}] (* _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, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, this sequence, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.
%Y Column 6 of A269924.
%Y Cf. A000108.
%K nonn
%O 13,1
%A _Gheorghe Coserea_, Jun 08 2017
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