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A127360
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a(n)=sum{k=0..n, C(n,floor(k/2))*4^(n-k)}.
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3
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1, 5, 22, 95, 406, 1730, 7360, 31295, 133030, 565430, 2403172, 10213670, 43408444, 184486580, 784069252, 3332296895, 14162266630, 60189642830, 255806000260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is (-3)^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)/(1-4x) 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))/(1-4*x*c(x^2))
a(n)= Sum_{k, 0<=k<=n} A061554(n,k)*4^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: A049675 A053154 A141222 * A116415 A026861 A026888
Adjacent sequences: A127357 A127358 A127359 * A127361 A127362 A127363
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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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