OFFSET
13,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
FORMULA
G.f.: 3*y*(y-1)^13*(224289558339*y^12 + 14578605290775*y^11 + 166145326384017*y^10 + 340348495329013*y^9 - 895516337370275*y^8 - 1061973836040211*y^7 + 2408646239898087*y^6 - 205280701572677*y^5 - 1466543072083650*y^4 + 763547357880930*y^3 - 17564852805804*y^2 - 51665824966088*y + 6399222484144)/(y-2)^38, 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) ((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}]);
a[n_] := Q[n, 4, 5];
Table[a[n], {n, 13, 27}] (* Jean-François Alcover, Oct 17 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 11 2017
STATUS
approved