A288287 a(n) is the number of rooted maps with n edges and 7 faces on an orientable surface of genus 5.

18475997006212200, 2595050050431235488, 178505550201444784920, 8127109896970086044280, 277921666244135490925320, 7658941714130456546009472, 177889367903895880526289600, 3591928999997575304490876960, 64495258714680679471831890624, 1047632171592441142843472246400, 15602830991918991492377865030768, 215367527001361085125596104693328

Offset

16,1

Links

Table of n, a(n) for n=16..27.

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

Formula

G.f.: -24*y*(y-1)^16*(2698126164350850*y^15 + 114214134208709301*y^14 + 1131272022789923528*y^13 + 2118653911175445143*y^12 - 7848128857296958637*y^11 - 10563945755997793403*y^10 + 30156692271220941375*y^9 + 1622522506032620085*y^8 - 39857153689058183268*y^7 + 24443452645454378385*y^6 + 6323328397994465472*y^5 - 10624874505421887856*y^4 + 2992426035154937504*y^3 + 122439286239701680*y^2 - 144788767567212992*y + 11962072115155008)/(y-2)^47, 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, 7, 5];
Table[a[n], {n, 16, 27}] (* 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, A288286 f=6, this sequence, A288288 f=8, A288289 f=9, A288290 f=10.

Column 7 of A269925.

Cf. A000108.

Sequence in context: A288280 A185434 A172655 * A349030 A083216 A180703

Adjacent sequences: A288284 A288285 A288286 * A288288 A288289 A288290

Keyword

nonn

Author

Gheorghe Coserea, Jun 11 2017

Status

approved