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A127362
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a(n)=sum(k=0..n, C(n,floor(k/2))*(-3)^(n-k)}.
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2
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1, -2, 8, -24, 84, -272, 920, -3040, 10180, -33840, 112968, -376224, 1254696, -4181088, 13939248, -46459584, 154873860, -516229040, 1720795880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is 4^n. In general, for r>=0, the sequence given by sum{k=0..n, C(n,floor(k/2))*(-r)^(n-k)} has Hankel transform (r+1)^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))
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CROSSREFS
| Sequence in context: A063727 A085449 * A133443 A094038 A007223 A106189
Adjacent sequences: A127359 A127360 A127361 * A127363 A127364 A127365
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
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