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 A045992 binomial(2n,n)-n; number of (weakly) increasing or decreasing maps from 1,...,n to 1,...,n. 5
 1, 1, 4, 17, 66, 247, 918, 3425, 12862, 48611, 184746, 705421, 2704144, 10400587, 40116586, 155117505, 601080374, 2333606203, 9075135282, 35345263781, 137846528800, 538257874419, 2104098963698, 8233430727577, 32247603683076 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 FORMULA G.f.: (x^2-(Sqrt[1-4*x]+2)*x+1)/(Sqrt[1-4*x]*(x-1)^2). - Harvey P. Dale, Apr 18 2014 EXAMPLE a(3)=17 since can map (1,2,3) to (1,1,1), (1,1,2), (1,1,3), (1,2,2), (1,2,3), (1,3,3), (2,1,1), (2,2,1), (2,2,2), (2,2,3), (2,3,3), (3,1,1), (3,2,1), (3,2,2), (3,3,1), (3,3,2), or (3,3,3) but not for example to (1,3,2) MATHEMATICA Table[Binomial[2n, n]-n, {n, 0, 30}] (* or *) CoefficientList[Series[ (x^2- (Sqrt[1-4 x]+2) x+1)/(Sqrt[1-4 x] (x-1)^2), {x, 0, 30}], x] (* Harvey P. Dale, Apr 18 2014 *) CROSSREFS Cf. A000312, A000984, A001700. Sequence in context: A181410 A102207 A202555 * A217539 A046723 A244616 Adjacent sequences:  A045989 A045990 A045991 * A045993 A045994 A045995 KEYWORD nonn AUTHOR STATUS approved

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