A288284 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 5.

4034735959800, 420797306522502, 21853758736216200, 762684674663536626, 20269771718252599536, 439591872915483185214, 8127109896970086044280, 131989618396827099239715, 1924446945220467632598816, 25606868770179512447281320, 314937862113457568812798944, 3616708980976267213715063568, 39101467996466899068672052800, 400687469703530771051452630260, 3913896712273232414650041609360

Offset: 13

Author

Gheorghe Coserea, Jun 11 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, A288282 f=2, A288283 f=3, this sequence, A288285 f=5, A288286 f=6, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.

Column 4 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, 4, 5];
Table[a[n], {n, 13, 27}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: 3*y*(y-1)^13*(224289558339*y^12 + 14578605290775*y^11 + 166145326384017*y^10 + 340348495329013*y^9 - 895516337370275*y^8 - 1061973836040211*y^7 + 2408646239898087*y^6 - 205280701572677*y^5 - 1466543072083650*y^4 + 763547357880930*y^3 - 17564852805804*y^2 - 51665824966088*y + 6399222484144)/(y-2)^38, where y=A000108(x).