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A288279
a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 4.
10
1763184571730010, 258634264294653390, 18451302662846918700, 866831237081712285138, 30468100266480917147760, 860337164444236894357488, 20423544863369526066131328, 420612140517667008915254376, 7689357064107454375292572788, 126977551039680427095997314540, 1920060399356995304343259728312
OFFSET
16,1
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)^16*(9225445001552610*y^15 + 253889174613116085*y^14 + 1531144661703557241*y^13 - 254390452688914375*y^12 - 11576322921612113581*y^11 + 5646113444605154169*y^10 + 28587502564009313669*y^9 - 31350769849259642447*y^8 - 9832935993984430480*y^7 + 29500732589692418132*y^6 - 12567984363713561312*y^5 - 2218978200544343392*y^4 + 2888444088307833216*y^3 - 630076702195212352*y^2 + 8436883230156800*y + 6263496930404352)/(y-2)^47, 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, 9, 4];
Table[a[n], {n, 16, 26}] (* Jean-François Alcover, Oct 16 2018 *)
CROSSREFS
Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, this sequence, A288280 f=10.
Column 9 of A269924.
Cf. A000108.
Sequence in context: A098099 A338442 A257138 * A318170 A204419 A067495
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved