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A104268
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2*4^(n-1) - (3n-1)/(2n+2)*C(2n,n).
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0
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1, 3, 12, 51, 218, 926, 3902, 16323, 67866, 280746, 1156576, 4748398, 19439332, 79391708, 323584322, 1316578403, 5348814842, 21702312818, 87955584152, 356114261498, 1440568977932, 5822909703908, 23520345224732
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Cardinality of the set of nesting-similarity classes.
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LINKS
| M. Klazar, On identities concerning the numbers of crossings and nestings of two edges in matchings
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FORMULA
| G.f.: C+z^2(2zC'+C)^2C, with C(z) the g.f. of the Catalan numbers.
G.f.: (x*(8*x+5*Sqrt[1-4 x]-9)-2*Sqrt[1-4 x]+2)/(2*(1-4*x)*x^2) [From Harvey P. Dale, Oct 03 2011]
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MATHEMATICA
| Table[2 4^(n-1)-(3n-1)/(2n+2) Binomial[2n, n], {n, 30}] (* From Harvey P. Dale, Oct 03 2011 *)
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CROSSREFS
| Equals A006419(n-1) + A000108(n).
Sequence in context: A135343 A083314 A155179 * A081704 A166482 A007854
Adjacent sequences: A104265 A104266 A104267 * A104269 A104270 A104271
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KEYWORD
| nonn,easy
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AUTHOR
| Ralf Stephan, Apr 17 2005
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