A288277 a(n) is the number of rooted maps with n edges and 7 faces on an orientable surface of genus 4.

17302190625720, 2089035241981688, 123981042854132536, 4892650539994184868, 145737674581607574840, 3515647035511186627416, 71823371612912533887168, 1281537868340178808063824, 20423544863369526066131328, 295680368360952875467454880, 3940377769373862621216994864

Offset: 14

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, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, this sequence, A288278 f=8, A288279 f=9, A288280 f=10.

Column 7 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, 7, 4];
Table[a[n], {n, 14, 24}] (* Jean-François Alcover, Oct 16 2018 *)

Formula

G.f.: -4*y*(y-1)^14*(18995313191166*y^13 + 602583747147072*y^12 + 3880832501643076*y^11 + 259447266126966*y^10 - 24577880734142257*y^9 + 10075843752456953*y^8 + 45406701745704921*y^7 - 44360505974166179*y^6 - 5860774604042624*y^5 + 22759971294835512*y^4 - 8598423383057104*y^3 - 18688742922288*y^2 + 464831946526080*y - 48608581644864)/(y-2)^41, where y=A000108(x).