A288286 a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 5.

1302772718028600, 166713517116449940, 10499075716384241952, 439591872915483185214, 13881153040572190501512, 354556747218700475500140, 7658941714130456546009472, 144282707675416905279319800, 2424036981927621898592714592, 36940703720927769833985462240, 517437278627390310406722691200, 6732676056022023909877001111172

Offset

15,1

Links

Table of n, a(n) for n=15..26.

Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

Formula

G.f.: 6*y*(y-1)^15*(282058698442290*y^14 + 13234659536432670*y^13 + 136523077378811396*y^12 + 265550247537056832*y^11 - 874424418903920099*y^10 - 1153574344496487459*y^9 + 3042269761791051489*y^8 + 35790516591815337*y^7 - 3265706341059162918*y^6 + 1932218163137003742*y^5 + 268611134157501684*y^4 - 531163056525180208*y^3 + 133718607048292896*y^2 - 1351891439085440*y - 1761044666234112)/(y-2)^44, where y=A000108(x).

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, 6, 5];
Table[a[n], {n, 15, 26}] (* Jean-François Alcover, Oct 17 2018 *)

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, A288284 f=4, A288285 f=5, this sequence, A288287 f=7, A288288 f=8, A288289 f=9, A288290 f=10.

Column 6 of A269925.

Cf. A000108.

Sequence in context: A072719 A185433 A134692 * A217683 A098099 A338442

Adjacent sequences: A288283 A288284 A288285 * A288287 A288288 A288289

Keyword

nonn

Author

Gheorghe Coserea, Jun 11 2017

Status

approved