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Search: id:A127362
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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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+0
3
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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; listen)
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OFFSET
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0,2
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COMMENT
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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
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G.f.: (1/sqrt(1-4x^2))(1+x*c(x^2))/(1+3*x*c(x^2))
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CROSSREFS
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Sequence in context: A034741 A085449 A063727 this_sequence A133443 A094038 A007223
Adjacent sequences: A127359 A127360 A127361 this_sequence A127363 A127364 A127365
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
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