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A288290 a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 5.

%I A288290 #14 Oct 17 2018 05:23:51
%S A288290 28449551653853229900,5131008990500486096250,447964809766718459342400,
%T A288290 25606868770179512447281320,1088463806617771584122226336,
%U A288290 36940703720927769833985462240,1047632171592441142843472246400,25624962301264473700614835484334,553279524558089394499396612588296,10733417717473916970871163704143300,189705897479950023040270728219928512
%N A288290 a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 5.
%H A288290 Gheorghe Coserea, <a href="/A288290/a288290.txt">The g.f. as a rational function of y=A000108(x)</a>
%H A288290 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.
%t A288290 Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
%t A288290 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 A288290 a[n_] := Q[n, 10, 5];
%t A288290 Table[a[n], {n, 19, 29}] (* _Jean-François Alcover_, Oct 17 2018 *)
%Y A288290 Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, this sequence.
%Y A288290 Column 10 of A269925.
%Y A288290 Cf. A000108.
%K A288290 nonn
%O A288290 19,1
%A A288290 _Gheorghe Coserea_, Jun 11 2017