login
A288287
a(n) is the number of rooted maps with n edges and 7 faces on an orientable surface of genus 5.
10
18475997006212200, 2595050050431235488, 178505550201444784920, 8127109896970086044280, 277921666244135490925320, 7658941714130456546009472, 177889367903895880526289600, 3591928999997575304490876960, 64495258714680679471831890624, 1047632171592441142843472246400, 15602830991918991492377865030768, 215367527001361085125596104693328
OFFSET
16,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
FORMULA
G.f.: -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
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 11 2017
STATUS
approved