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A288284 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 5.

%I A288284 #15 Oct 17 2018 12:32:20
%S A288284 4034735959800,420797306522502,21853758736216200,762684674663536626,
%T A288284 20269771718252599536,439591872915483185214,8127109896970086044280,
%U A288284 131989618396827099239715,1924446945220467632598816,25606868770179512447281320,314937862113457568812798944,3616708980976267213715063568,39101467996466899068672052800,400687469703530771051452630260,3913896712273232414650041609360
%N A288284 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 5.
%H A288284 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 A288284 G.f.: 3*y*(y-1)^13*(224289558339*y^12 + 14578605290775*y^11 + 166145326384017*y^10 + 340348495329013*y^9 - 895516337370275*y^8 - 1061973836040211*y^7 + 2408646239898087*y^6 - 205280701572677*y^5 - 1466543072083650*y^4 + 763547357880930*y^3 - 17564852805804*y^2 - 51665824966088*y + 6399222484144)/(y-2)^38, where y=A000108(x).
%t A288284 Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
%t A288284 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 A288284 a[n_] := Q[n, 4, 5];
%t A288284 Table[a[n], {n, 13, 27}] (* _Jean-François Alcover_, Oct 17 2018 *)
%Y A288284 Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, this sequence, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
%Y A288284 Column 4 of A269925.
%Y A288284 Cf. A000108.
%K A288284 nonn
%O A288284 13,1
%A A288284 _Gheorghe Coserea_, Jun 11 2017