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A127363
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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, -3, 14, -57, 246, -1038, 4424, -18777, 79846, -339258, 1442004, -6128202, 26045436, -110691948, 470442924, -1999378137, 8497365126, -36113785698
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is 5^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+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))
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CROSSREFS
| Sequence in context: A135926 A015523 * A133444 A126875 A110526 A038679
Adjacent sequences: A127360 A127361 A127362 * A127364 A127365 A127366
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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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