A288282 a(n) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus 5.

4304016990, 354949166565, 14805457339920, 420797306522502, 9220982517965400, 166713517116449940, 2595050050431235488, 35801820369640556595, 447016944351510642564, 5131008990500486096250, 54801783386722932356160, 549865627271249187555384, 5223273162178751507973600

Offset: 11

Author

Gheorghe Coserea, Jun 09 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 5 with n edges and f faces for 1<=f<=10: A288281 f=1, this sequence, A288283 f=3, A288284 f=4, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.

Column 2 of A269925.

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, 2, 5];
Table[a[n], {n, 11, 23}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: 3*y*(y-1)^11*(19840275*y^10 + 3054079665*y^9 + 39932223996*y^8 + 81871857210*y^7 - 177595619343*y^6 - 160148276767*y^5 + 319799274321*y^4 - 57293265711*y^3 - 75145589046*y^2 + 28452476366*y - 1512328636)/(y-2)^32, where y=A000108(x).