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A127359
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a(n)=sum{k=0..n, C(n,floor(k/2))*3^(n-k)}.
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4
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1, 4, 14, 48, 162, 544, 1820, 6080, 20290, 67680, 225684, 752448, 2508468, 8362176, 27875064, 92919168, 309734850, 1032458080, 3441543140, 11471842880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is (-2)^n. In general, given r>=0, the sequence given by sum{k=0..n, C(n,floor(k/2))*r^(n-k)} has Hankel transform (1-r)^n. The sequence is the image of the sequence with g.f. (1+x)/(1-3x) under the Chebyshev mapping g(x)->(1/sqrt(1-4x^2))g(xc(x^2)), where c(x) is the g.f. of the Catalan numbers A000108.
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FORMULA
| G.f.: (1/sqrt(1-4x^2))(1+x*c(x^2))/(1-3*x*c(x^2))
a(n)= Sum_{k, 0<=k<=n} A061554(n,k)*3^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 04 2009]
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CROSSREFS
| Cf. A107430 [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 16 2009]
Sequence in context: A022632 A027906 A047135 * A007070 A204089 A092489
Adjacent sequences: A127356 A127357 A127358 * A127360 A127361 A127362
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
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