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Search: id:A100320
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| A100320 |
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A Catalan transform of (1+2x)/(1-2x). |
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+0
8
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| 1, 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; listen)
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OFFSET
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0,2
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COMMENT
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A Catalan transform of (1+2x)/(1-2x) under the mapping g(x)->g(xc(x)). The original sequence can be retrieved by g(x)->g(x(1-x)).
T(2n,n) for the triangle A132046. Hankel transform is A144704. [From Paul Barry (pbarry(AT)wit.ie), Sep 19 2008]
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FORMULA
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G.f.: (1+2xc(x))/(1-2xc(x)) where c(x) is the g.f. of A000108; a(n)=4*binomial(2n-1, n)-3*0^n; a(n)=binomial(2n, n)(4*2^(n-1)-0^n)/2^n; a(n)=sum{j=0..n, sum{k=0..n, C(2n, n-k)((2k+1)/(n+k+1))C(k, j)(-1)^(j-k)*(4*2^(j-1)-0^j)}}.
a(n)=A028329(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2008]
a(n)=Sum_{k, 0<=k<=n} A039599(n,k)*A010684(k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2008]
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CROSSREFS
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Sequence in context: A087206 A081875 A102433 this_sequence A064649 A149332 A149333
Adjacent sequences: A100317 A100318 A100319 this_sequence A100321 A100322 A100323
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 14 2004
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EXTENSIONS
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Incorrect connection with A046055 deleted by N. J. A. Sloane, Jul 08 2009
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