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.: 2*y*(y-1)^13*(1208305403982*y^12 + 42344287039512*y^11 + 283047148578040*y^10 + 47183718440672*y^9 - 1618438221531593*y^8 + 617910272368381*y^7 + 2488374601412831*y^6 - 2268379207704481*y^5 - 116197489174642*y^4 + 764144804102008*y^3 - 252877960850800*y^2 + 8651012216320*y + 3769026206720)/(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)((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, 6, 4];
Table[a[n], {n, 13, 24}] (* Jean-François Alcover, Oct 16 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved