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A085990
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Number of topological types of polygons with 2n different sides.
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1
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0, 3, 60, 2520, 181440, 19958400, 3113510400, 653837184000, 177843714048000, 60822550204416000, 25545471085854720000, 12926008369442488320000, 7755605021665492992000000, 5444434725209176080384000000, 4420880996869850977271808000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) equals (-1)^n times the coefficient of sqrt(1-x^2)*(arcsin x)^2 in int (arcsin x)^(2n-1) dx. [From John M. Campbell, Jul 20 2011]
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FORMULA
| a(n) = (n-1)*(2*n-1)*(2*n-3)!
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EXAMPLE
| For example: if n=1 then no polygon exists with 2 different sides. If n=2 then the polygon has 4 different sides A, B, C, D. In this case 3 different types of such 4-angle exist: (A, B, C, D), (A, B, D, C), (A, C, B, D).
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MATHEMATICA
| nn = 32; a = Log[1/(1 - x^2)^(1/4)] - x^2/4; Prepend[Select[Range[0, nn]! CoefficientList[Series[a, {x, 0, nn}], x], # > 0 &], 0] (* Geoffrey Critzer, Dec 10 2011 *)
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PROG
| (PARI) a(n)=(2*n-1)!\2 \\ Charles R Greathouse IV, Dec 10 2011
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CROSSREFS
| Sequence in context: A001084 A137150 A081854 * A202065 A036770 A201699
Adjacent sequences: A085987 A085988 A085989 * A085991 A085992 A085993
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KEYWORD
| nonn,easy
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AUTHOR
| Sergey.L.Dolmatov, Almir Dzhumaev (aalma(AT)mail.ru), Aug 18 2003
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