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A288277
a(n) is the number of rooted maps with n edges and 7 faces on an orientable surface of genus 4.
10
17302190625720, 2089035241981688, 123981042854132536, 4892650539994184868, 145737674581607574840, 3515647035511186627416, 71823371612912533887168, 1281537868340178808063824, 20423544863369526066131328, 295680368360952875467454880, 3940377769373862621216994864
OFFSET
14,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
FORMULA
G.f.: -4*y*(y-1)^14*(18995313191166*y^13 + 602583747147072*y^12 + 3880832501643076*y^11 + 259447266126966*y^10 - 24577880734142257*y^9 + 10075843752456953*y^8 + 45406701745704921*y^7 - 44360505974166179*y^6 - 5860774604042624*y^5 + 22759971294835512*y^4 - 8598423383057104*y^3 - 18688742922288*y^2 + 464831946526080*y - 48608581644864)/(y-2)^41, 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) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 2) (2n - 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] (2k - 1) (2l - 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, 4];
Table[a[n], {n, 14, 24}] (* Jean-François Alcover, Oct 16 2018 *)
CROSSREFS
Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, this sequence, A288278 f=8, A288279 f=9, A288280 f=10.
Column 7 of A269924.
Cf. A000108.
Sequence in context: A349028 A160935 A159271 * A297449 A321137 A064589
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved