A288271 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 4.

225225, 12317877, 351683046, 7034538511, 111159740692, 1480593013900, 17302190625720, 182231849209410, 1763184571730010, 15894791312284170, 134951136993773100, 1088243826731751690, 8391311316938069520, 62210659883935683120, 445441857820701181440, 3092035882104030618900

Offset

8,1

Links

Table of n, a(n) for n=8..23.

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

Adjacent sequences: A288268 A288269 A288270 * A288272 A288273 A288274

Keyword

nonn

Author

Gheorghe Coserea, Jun 08 2017

Status

approved