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Search: id:A127361
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| A127361 |
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a(n)=sum(k=0..n, C(n,floor(k/2))*(-2)^(n-k)}. |
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+0
7
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| 1, -1, 4, -7, 22, -46, 130, -295, 790, -1870, 4864, -11782, 30148, -73984, 187534, -463687, 1168870, -2902870, 7293640, -18161170, 45541492, -113576596
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Hankel transform is 3^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+2x) 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.
Second binomial transform is A026641 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 14 2007
Signed version of A100098 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 25 2007
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FORMULA
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G.f.: (1/sqrt(1-4x^2))(1+x*c(x^2))/(1+2*x*c(x^2))
a(n) = Sum_{k, 0<=k<=n} A061554(n,k)*(-2)^k . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 25 2007
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CROSSREFS
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Sequence in context: A010363 A119561 A026548 this_sequence A100098 A128533 A126094
Adjacent sequences: A127358 A127359 A127360 this_sequence A127362 A127363 A127364
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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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