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Search: id:A127358
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| A127358 |
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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, 3, 8, 21, 54, 138, 350, 885, 2230, 5610, 14088, 35346, 88596, 221952, 555738, 1391061, 3480870, 8708610, 21783680, 54483510, 136254964, 340729788, 852000828, 2130354786, 5326563004
(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 (-1)^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)/(1-2x) 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.
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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)=2*a(n-1)+A054341(n-1). a(n)=Sum_{k, 0<=k<=n}A126075(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 03 2007
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CROSSREFS
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Sequence in context: A030015 A103446 A094723 this_sequence A077849 A135473 A005580
Adjacent sequences: A127355 A127356 A127357 this_sequence A127359 A127360 A127361
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 11 2007
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