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A288289 a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 5.

%I A288289 #13 Oct 17 2018 05:23:43
%S A288289 2682208751185413450,447016944351510642564,36188783145801243558900,
%T A288289 1924446945220467632598816,76330117260895762678976496,
%U A288289 2424036981927621898592714592,64495258714680679471831890624,1483610943246601143976044602400,30193909664655985735143003641892,553279524558089394499396612588296,9254922250232295721515866705613000,142890407229849701818261896174135456
%N A288289 a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 5.
%H A288289 Gheorghe Coserea, <a href="/A288289/a288289.txt">The g.f. as a rational function of y=A000108(x)</a>
%H A288289 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 A288289 Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
%t A288289 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 A288289 a[n_] := Q[n, 9, 5];
%t A288289 Table[a[n], {n, 18, 29}] (* _Jean-François Alcover_, Oct 17 2018 *)
%Y A288289 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, this sequence, A288290 f=10.
%Y A288289 Column 9 of A269925.
%Y A288289 Cf. A000108.
%K A288289 nonn
%O A288289 18,1
%A A288289 _Gheorghe Coserea_, Jun 11 2017