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A288278
a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 4.
10
182231849209410, 24325590127655531, 1587135819804394530, 68503375296263488977, 2221381417843144801098, 58089920897558352891672, 1281537868340178808063824, 24605894500188479477960928, 420612140517667008915254376, 6512251870890866709301451550, 92559480623350598649493386580
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.: y*(y-1)^15*(2141204115631518*y^14 + 62802256981978404*y^13 + 390904315702808387*y^12 - 17469926941849537*y^11 - 2715522908192830943*y^10 + 1209526054185992549*y^9 + 5862111891800632315*y^8 - 6084780630540788053*y^7 - 1344178041537337418*y^6 + 4359417524034703460*y^5 - 1779344954166712472*y^4 - 128701285301543888*y^3 + 220665627694548576*y^2 - 38233669153240512*y + 844773167217024)/(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) ((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, 8, 4];
Table[a[n], {n, 15, 25}] (* 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, A288277 f=7, this sequence, A288279 f=9, A288280 f=10.
Column 8 of A269924.
Cf. A000108.
Sequence in context: A245721 A320874 A348801 * A172566 A214947 A364413
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved