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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
OFFSET
12,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
FORMULA
G.f.: -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];
Table[a[n], {n, 12, 24}] (* Jean-François Alcover, Oct 17 2018 *)
CROSSREFS
Rooted maps of genus 5 with n edges and f faces for 1<=f<=10: A288281 f=1, A288282 f=2, this sequence, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.
Column 3 of A269925.
Cf. A000108.
Sequence in context: A290122 A234379 A290157 * A271819 A304235 A233503
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 09 2017
STATUS
approved