OFFSET
11,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
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, 3];
Table[a[n], {n, 11, 28}] (* Jean-François Alcover, Oct 17 2018 *)
PROG
(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288080_ser(N) = {
my(y = A000108_ser(N+1));
2*y*(y-1)^11*(2360692395*y^10 + 57065162931*y^9 + 200199438395*y^8 - 321653197109*y^7 - 594662939878*y^6 + 999754510326*y^5 - 90653073868*y^4 - 435707439920*y^3 + 201952082336*y^2 - 14180151168*y - 3375786240)/(y-2)^32;
};
Vec(A288080_ser(15))
CROSSREFS
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 07 2017
STATUS
approved