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A118449
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Number of rooted n-edge one-vertex maps on a non-orientable genus-4 surface (dually: one-face maps).
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2
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0, 488, 11660, 160680, 1678880, 14771680, 115457832, 827303280, 5545466520, 35257287120, 214730922120, 1262004908528, 7197437563680, 40007524376960, 217501266966160, 1159737346931040, 6079078540464072, 31385516059734960
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OFFSET
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3,2
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COMMENTS
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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).
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REFERENCES
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E. R. Canfield, Calculating the number of rooted maps on a surface, Congr. Numerantium, 76 (1990), 21-34.
D. M. Jackson and T. I. Visentin, An atlas of the smaller maps in orientable and nonorientable surfaces. CRC Press, Boca Raton, 2001.
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LINKS
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FORMULA
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O.g.f.: -(R-1)^4(R+1)^3(65R^3+337R^2-433R-945)/256R^11, where R=sqrt(1-4x).
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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