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%I #14 Oct 17 2018 05:23:35
%S 233454817237201560,35801820369640556595,2677324515710001081372,
%T 131989618396827099239715,4869474711666664850333856,
%U 144282707675416905279319800,3591928999997575304490876960,77515666515764938993111323048,1483610943246601143976044602400,25624962301264473700614835484334,404881818003827869935873694190904,5916336815178383154031082792690874
%N a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 5.
%H Gheorghe Coserea, <a href="/A288288/a288288.txt">The g.f. as a rational function of y=A000108(x)</a>
%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.
%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, 8, 5];
%t Table[a[n], {n, 17, 28}] (* _Jean-François Alcover_, Oct 17 2018 *)
%Y 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, this sequence, A288289 f=9, A288290 f=10.
%Y Column 8 of A269925.
%Y Cf. A000108.
%K nonn
%O 17,1
%A _Gheorghe Coserea_, Jun 11 2017
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