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A288271
a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 4.
10
225225, 12317877, 351683046, 7034538511, 111159740692, 1480593013900, 17302190625720, 182231849209410, 1763184571730010, 15894791312284170, 134951136993773100, 1088243826731751690, 8391311316938069520, 62210659883935683120, 445441857820701181440, 3092035882104030618900
OFFSET
8,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
FORMULA
G.f.: -143*y*(y-1)^8*(1575*y^6 + 13689*y^5 + 4689*y^4 - 34417*y^3 + 11361*y^2 + 7017*y - 2339)/(y-2)^23, 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, 1, 4];
Table[a[n], {n, 8, 23}] (* Jean-François Alcover, Oct 16 2018 *)
PROG
(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288271_ser(N) = {
my(y = A000108_ser(N+1));
-143*y*(y-1)^8*(1575*y^6 + 13689*y^5 + 4689*y^4 - 34417*y^3 + 11361*y^2 + 7017*y - 2339)/(y-2)^23;
};
Vec(A288271_ser(16))
CROSSREFS
Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: this sequence, A288272 f=2, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.
Column 1 of A269924.
Cf. A000108.
Sequence in context: A252394 A237848 A269924 * A215402 A204743 A048427
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved