A288281 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 5.

59520825, 4304016990, 158959754226, 4034735959800, 79553497760100, 1302772718028600, 18475997006212200, 233454817237201560, 2682208751185413450, 28449551653853229900, 281858111998039476900, 2632472852850938916000, 23350616705746908461520, 197910970615681824664800, 1610886016462484019585600

Offset: 10

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: this sequence, A288282 f=2, 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 1 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, 1, 5];
Table[a[n], {n, 10, 24}] (* Jean-François Alcover, Oct 17 2018 *)

Formula

G.f.: -88179*y*(y-1)^10*(675*y^8 + 9660*y^7 + 19104*y^6 - 38620*y^5 - 26606*y^4 + 51308*y^3 - 10784*y^2 - 5416*y + 1354)/(y-2)^29, where y=A000108(x).