A288280 a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 4.

15894791312284170, 2548272396065512974, 197822824662547694148, 10071757699155275906824, 382217975972687580876304, 11612741439751867739074432, 295680368360952875467454880, 6512251870890866709301451550, 126977551039680427095997314540, 2230836871835420574103711453068

Offset: 17

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, A288277 f=7, A288278 f=8, A288279 f=9, this sequence.

Column 10 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) (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] (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, 10, 4];
Table[a[n], {n, 17, 26}] (* Jean-François Alcover, Oct 16 2018 *)

Formula

G.f.: 2*y*(y-1)^17*(667113335854505289*y^16 + 17412039201241985652*y^15 + 101949739105950626070*y^14 - 30202970169901595562*y^13 - 833532476362240891879*y^12 + 447114036864981439647*y^11 + 2316066844919602997013*y^10 - 2673632819222127570107*y^9 - 1088786810085394834566*y^8 + 3157924186313124711792*y^7 - 1371258409341666011952*y^6 - 433458368694714259536*y^5 + 515333809963509426144*y^4 - 126279314363368987008*y^3 - 3637814234318456832*y^2 + 4694513255143047936*y - 365353090019990016)/(y-2)^50, where y=A000108(x).