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A288075
a(n) is the number of rooted maps with n edges and one face on an orientable surface of genus 3.
10
1485, 56628, 1169740, 17454580, 211083730, 2198596400, 20465052608, 174437377400, 1384928666550, 10369994005800, 73920866362200, 505297829133240, 3331309741059300, 21280393666593600, 132216351453357600, 801482122777393200, 4752780295205269470, 27632111202537355800
OFFSET
6,1
LINKS
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
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 07 2017
STATUS
approved