|
|
A288285
|
|
a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 5.
|
|
10
|
|
|
79553497760100, 9220982517965400, 528887751025584600, 20269771718252599536, 588564117958709029644, 13881153040572190501512, 277921666244135490925320, 4869474711666664850333856, 76330117260895762678976496, 1088463806617771584122226336, 14304840156674599302991391808, 175067544404400195382759080000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
14,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -12*y*(y-1)^14*(3140032216620*y^13 + 168745438117215*y^12 + 1823095410398560*y^11 + 3655757687054272*y^10 - 10735527168335100*y^9 - 13611993085165141*y^8 + 33238393245141476*y^7 - 1171322344070974*y^6 - 27716201280764020*y^5 + 15575605858027959*y^4 + 683444198956148*y^3 - 2374578542797076*y^2 + 479239083620192*y - 11169074253456)/(y-2)^41, 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, 5, 5];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|