OFFSET
16,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
FORMULA
G.f.: -6*y*(y-1)^16*(9225445001552610*y^15 + 253889174613116085*y^14 + 1531144661703557241*y^13 - 254390452688914375*y^12 - 11576322921612113581*y^11 + 5646113444605154169*y^10 + 28587502564009313669*y^9 - 31350769849259642447*y^8 - 9832935993984430480*y^7 + 29500732589692418132*y^6 - 12567984363713561312*y^5 - 2218978200544343392*y^4 + 2888444088307833216*y^3 - 630076702195212352*y^2 + 8436883230156800*y + 6263496930404352)/(y-2)^47, where y=A000108(x).
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, 9, 4];
Table[a[n], {n, 16, 26}] (* Jean-François Alcover, Oct 16 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved