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Search: id:A001246
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| A001246 |
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Squares of Catalan numbers. |
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+0
18
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| 1, 1, 4, 25, 196, 1764, 17424, 184041, 2044900, 23639044, 282105616, 3455793796, 43268992144, 551900410000, 7152629313600, 93990019574025, 1250164827828900, 16807771574144100, 228138727737690000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also multi-component meanders.
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REFERENCES
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O. Guibert, Stack words, ..., Discr. Math., 210 (2000), 71-85.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
P. Di Francesco, O. Golinelli and E. Guitter, Meander, folding and arch statistics.
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FORMULA
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G.f.: -1/(4*x)+1/2*(16*x-1)/x*EllipticK(4*x^(1/2))/Pi+1/x*EllipticE(4*x^(1/2))/Pi. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 12 2003
E.g.f.: hypergeom([1/2], [2, 2], 4*x^2) = 2*BesselI(0, 2*x)^2-BesselI(0, 2*x)*BesselI(1, 2*x)/x-2*BesselI(1, 2*x)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 04 2005
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MAPLE
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seq((binomial(2*n, n)/(1+n))^2, n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 2007
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PROGRAM
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(Mupad) combinat::dyckWords::count(n)^2 $ n = 0..18 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 15 2007
(Other) sage: [catalan_number(i)^2 for i in xrange(0, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009]
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CROSSREFS
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Cf. A000108.
Row sums of triangle A008828.
Sequence in context: A060908 A036449 A051500 this_sequence A151342 A065735 A140094
Adjacent sequences: A001243 A001244 A001245 this_sequence A001247 A001248 A001249
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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