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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

N. J. A. Sloane.

STATUS

approved

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Last modified December 21 20:00 EST 2014. Contains 252326 sequences.