A288075 a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 3.

1485, 56628, 1169740, 17454580, 211083730, 2198596400, 20465052608, 174437377400, 1384928666550, 10369994005800, 73920866362200, 505297829133240, 3331309741059300, 21280393666593600, 132216351453357600, 801482122777393200, 4752780295205269470, 27632111202537355800

Offset

6,1

Links

Table of n, a(n) for n=6..23.

Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

Mathematica

A000108ser[n_] := (1 - Sqrt[1 - 4*x])/(2*x) + O[x]^(n+1);
A288075ser[n_] := (y = A000108ser[n+1]; -11*y*(y-1)^6*(135*y^4 + 558*y^3 - 400*y^2 - 316*y + 158)/(y-2)^17);
Drop[CoefficientList[A288075ser[20], x], 6] (* Jean-François Alcover, Jun 13 2017, translated from PARI *)

Prog

(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288075_ser(N) = {
  my(y = A000108_ser(N+1));
  -11*y*(y-1)^6*(135*y^4 + 558*y^3 - 400*y^2 - 316*y + 158)/(y-2)^17;
};
Vec(A288075_ser(18))

Crossrefs

Rooted maps of genus 3 with n edges and f faces for 1<=f<=10: this sequence, A288076 f=2, A288077 f=3, A288078 f=4, A288079 f=5, A288080 f=6, A288081 f=7, A288262 f=8, A288263 f=9, A288264 f=10.

Column 1 of A269923, column 3 of A035309.

Cf. A000108.

Sequence in context: A327880 A257713 A269923 * A104742 A278853 A051260

Adjacent sequences: A288072 A288073 A288074 * A288076 A288077 A288078

Keyword

nonn

Author

Gheorghe Coserea, Jun 07 2017

Status

approved