
MATHEMATICA

Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0  f < 0  g < 0 = 0;
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}]);
a[n_] := Q[n, 8, 5];
Table[a[n], {n, 17, 28}] (* JeanFrançois Alcover, Oct 17 2018 *)


CROSSREFS

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.
Column 8 of A269925.
Cf. A000108.
Sequence in context: A094676 A327760 A054213 * A080128 A132901 A058292
Adjacent sequences: A288285 A288286 A288287 * A288289 A288290 A288291
