login
A288286
a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 5.
10
1302772718028600, 166713517116449940, 10499075716384241952, 439591872915483185214, 13881153040572190501512, 354556747218700475500140, 7658941714130456546009472, 144282707675416905279319800, 2424036981927621898592714592, 36940703720927769833985462240, 517437278627390310406722691200, 6732676056022023909877001111172
OFFSET
15,1
LINKS
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
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 11 2017
STATUS
approved