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%I #14 Oct 16 2018 13:49:12
%S 7034538511,600398249550,25766235457300,750260619502310,
%T 16789118602155860,309197871098871838,4892650539994184868,
%U 68503375296263488977,866831237081712285138,10071757699155275906824,108780460548715291414960,1102776421660293787585728,10575907938883627723298512,96567859695821049858887188,844021580327996006292420440
%N a(n) is the number of rooted maps with n edges and 4 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)^11*(1495900107*y^10 + 72057286944*y^9 + 525358145917*y^8 + 168001652997*y^7 - 2349735380723*y^6 + 817302422933*y^5 + 2199510551627*y^4 - 1660311974101*y^3 + 109057768182*y^2 + 147825658668*y - 23527494040)/(y-2)^32, 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, 4, 4];
%t Table[a[n], {n, 11, 25}] (* _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, this sequence, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.
%Y Column 4 of A269924.
%Y Cf. A000108.
%K nonn
%O 11,1
%A _Gheorghe Coserea_, Jun 08 2017
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