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A288085
a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 2.
9
570570, 34374186, 1059255456, 22555934280, 375708427812, 5235847653036, 63648856688592, 694146691745820, 6928413234959820, 64232028100704156, 559373367462490656, 4616545437250956192, 36362952155187558600, 274925536462366808760, 2004633652255211204832, 14152391716870383219492
OFFSET
8,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
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, 5, 2];
Table[a[n], {n, 8, 23}] (* Jean-François Alcover, Oct 18 2018 *)
PROG
(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288085_ser(N) = {
my(y = A000108_ser(N+1));
-6*y*(y-1)^8*(108346*y^7 + 1760421*y^6 + 1641979*y^5 - 7296839*y^4 + 2560152*y^3 + 2713196*y^2 - 1525104*y + 132944)/(y-2)^23;
};
Vec(A288085_ser(16))
CROSSREFS
Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, A288082 f=2, A288083 f=3, A288084 f=4, this sequence, A288086 f=6, A288087 f=7, A288088 f=8, A288089 f=9, A288090 f=10.
Column 5 of A269922, column 2 of A270409.
Cf. A000108.
Sequence in context: A156412 A068724 A233651 * A121169 A237173 A090061
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 05 2017
STATUS
approved