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%I #18 Oct 27 2024 05:34:02
%S 0,488,11660,160680,1678880,14771680,115457832,827303280,5545466520,
%T 35257287120,214730922120,1262004908528,7197437563680,40007524376960,
%U 217501266966160,1159737346931040,6079078540464072,31385516059734960
%N Number of rooted n-edge one-vertex maps on a non-orientable genus-4 surface (dually: one-face maps).
%C One-vertex maps on a non-orientable genus-3 surface are counted by A118448. Such maps are also called bouquets of loops (and their duals are called unicellular maps).
%D E. R. Canfield, Calculating the number of rooted maps on a surface, Congr. Numerantium, 76 (1990), 21-34.
%D D. M. Jackson and T. I. Visentin, An atlas of the smaller maps in orientable and nonorientable surfaces. CRC Press, Boca Raton, 2001.
%H Didier Arquès and Alain Giorgetti, <a href="https://doi.org/10.1016/S0304-3975(98)00230-8">Counting rooted maps on a surface</a>, Theoret. Comput. Sci. 234 (2000), no. 1-2, 255--272. MR1745078 (2001f:05078).
%F O.g.f.: -(R-1)^4(R+1)^3(65R^3+337R^2-433R-945)/(256R^11), where R=sqrt(1-4x).
%F a(n) ~ n^(9/2) * 2^(2*n-3) / sqrt(Pi) * (1 - 2*sqrt(Pi)/(3*sqrt(n))). - _Vaclav Kotesovec_, Oct 27 2024
%t With[{r=Sqrt[1-4x]},Drop[CoefficientList[Series[-(r-1)^4 (r+1)^3 (65r^3+ 337r^2- 433r-945)/(256r^11),{x,0,20}],x],3]] (* _Harvey P. Dale_, Aug 05 2019 *)
%Y Cf. A118448. A diagonal of A214806.
%K nonn
%O 3,2
%A _Valery A. Liskovets_, May 04 2006