A288272 a(n) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus 4.

12317877, 792534015, 26225260226, 600398249550, 10743797911132, 160576594766588, 2089035241981688, 24325590127655531, 258634264294653390, 2548272396065512974, 23532893106071038404, 205518653220527665304, 1709552077642556424368, 13623964536133602210560, 104522878918062035228512

Offset: 9

Author

Gheorghe Coserea, Jun 08 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 4 with n edges and f faces for 1<=f<=10: A288271 f=1, this sequence, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.

Column 2 of A269924.

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)((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, 2, 4];
Table[a[n], {n, 9, 23}] (* Jean-François Alcover, Oct 16 2018 *)

Formula

G.f.: y*(y-1)^9*(225225*y^8 + 25467156*y^7 + 207300366*y^6 + 77853486*y^5 - 660073489*y^4 + 222312257*y^3 + 269246651*y^2 - 140048085*y + 10034310)/(y-2)^26, where y=A000108(x).