A288089 a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 2.

1293938646, 140725699686, 7454157823560, 261637840342860, 6928413234959820, 148755268498286436, 2710382626755160416, 43241609165618454096, 617910462111714896820, 8044640800289827566756, 96690983139765469347024, 1084226645505246141589704, 11439196912435362172792536, 114351801899024314438876200

Offset: 12

Author

Gheorghe Coserea, Jun 05 2017

Keywords

• nonn

Links

• Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

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, A288087 f=7, A288088 f=8, this sequence, A288090 f=10.

Column 9 of A269922.

Cf. A000108.

Programs

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, 9, 2];
Table[a[n], {n, 12, 25}] (* Jean-François Alcover, Oct 18 2018 *)

PARI

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288089_ser(N) = {
  my(y = A000108_ser(N+1));
  -6*y*(y-1)^12*(12205186004*y^11 + 144345246789*y^10 + 83883548039*y^9 - 978172313331*y^8 + 436600889944*y^7 + 1435650005364*y^6 - 1511798886368*y^5 + 121539026592*y^4 + 411304907520*y^3 - 171035694144*y^2 + 14120686592*y + 1573053440)/(y-2)^35;
};
Vec(A288089_ser(13))