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A028329
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Twice central binomial coefficients.
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8
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2, 4, 12, 40, 140, 504, 1848, 6864, 25740, 97240, 369512, 1410864, 5408312, 20801200, 80233200, 310235040, 1202160780, 4667212440, 18150270600, 70690527600, 275693057640, 1076515748880, 4208197927440, 16466861455200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Central elements in the even-Pascal triangle A028326.
If Y is a 3-subset of an 2n-set X then, for n>=3, a(n-1) is the number of (n+1)-subsets of X having at least two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 16 2007
a(n) denotes the number of ways one can reach the (n,n) point in an n X n grid via the point (n-1, n-1) starting from (0,0) when moving right and up is allowed [From Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 29 2009]
It appears that a(n-1) is also the number of quivers in the mutation class of twisted types BD_n and CD_n for n>=3. [From Christian Stump (christian.stump(AT)gmail.com), Nov 03 2010]
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
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FORMULA
| G.f.: 2/sqrt(1-4x). a(n)=2*binomial(2n, n).
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MAPLE
| seq(sum(binomial(2*n, n), k=1..2), n=0..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2007
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MATHEMATICA
| Table[2Binomial[2n, n], {n, 0, 30}] (* From Harvey P. Dale, Aug 08 2011 *)
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PROG
| (PARI) a(n)=2*binomial(2*n, n)
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CROSSREFS
| a(n)=2*A000984(n).
Bisection of A047073, A063886. First differences of A054113.
Sequence in context: A126946 A113179 A056236 * A204678 A025227 A119430
Adjacent sequences: A028326 A028327 A028328 * A028330 A028331 A028332
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KEYWORD
| nonn,easy
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AUTHOR
| Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu)
Edited by Michael Somos, Sep 13 2003
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