OFFSET
10,1
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)^10*(12317877*y^9 + 793781118*y^8 + 6094043038*y^7 + 2216299748*y^6 - 23375789497*y^5 + 7963356801*y^4 + 15368481377*y^3 - 10027219339*y^2 + 877859200*y + 252711200)/(y-2)^29, 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, 3, 4];
Table[a[n], {n, 10, 24}] (* Jean-François Alcover, Oct 16 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved