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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 (list; graph; refs; listen; history; text; internal format)
 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 Adjacent sequences:  A288072 A288073 A288074 * A288076 A288077 A288078 KEYWORD nonn AUTHOR Gheorghe Coserea, Jun 07 2017 STATUS approved

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Last modified June 23 08:44 EDT 2021. Contains 345395 sequences. (Running on oeis4.)