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A288087
a(n) is the number of rooted maps with n edges and 7 faces on an orientable surface of genus 2.
9
31039008, 2583699888, 106853266632, 2979641557620, 63648856688592, 1117259292848016, 16842445235560944, 224686278407291148, 2710382626755160416, 30044423965980553536, 309859885439753598768, 3002524783711124880936, 27551689577648333614176, 240961534103705377359840, 2019318707410947848445792
OFFSET
10,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
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, 7, 2];
Table[a[n], {n, 10, 24}] (* Jean-François Alcover, Oct 18 2018 *)
PROG
(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288087_ser(N) = {
my(y = A000108_ser(N+1));
-12*y*(y-1)^10*(20697615*y^9 + 275716321*y^8 + 211910021*y^7 - 1514443109*y^6 + 601694224*y^5 + 1328709592*y^4 - 1136750032*y^3 + 153705072*y^2 + 76788992*y - 15442112)/(y-2)^29;
};
Vec(A288087_ser(15))
CROSSREFS
Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, A288082 f=2, A288083 f=3, A288084 f=4, A288085 f=5, A288086 f=6, this sequence, A288088 f=8, A288089 f=9, A288090 f=10.
Column 7 of A269922, column 2 of A270411.
Cf. A000108.
Sequence in context: A205272 A261986 A103576 * A203276 A182088 A209786
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 05 2017
STATUS
approved