|
|
A288283
|
|
a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 5.
|
|
10
|
|
|
158959754226, 14805457339920, 691650582088536, 21853758736216200, 528887751025584600, 10499075716384241952, 178505550201444784920, 2677324515710001081372, 36188783145801243558900, 447964809766718459342400, 5141788096308757330278816, 55267879542927003057175200, 560775739552815581754138816
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
12,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -6*y*(y-1)^12*(1434672330*y^11 + 125297167569*y^10 + 1520299523980*y^9 + 3143130463894*y^8 - 7464422123238*y^7 - 7957464673806*y^6 + 16850577489362*y^5 - 2273292547090*y^4 - 6843677356968*y^3 + 3164962758706*y^2 - 181381616688*y - 58970465680)/(y-2)^35, 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, 3, 5];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|