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Search: id:A100098
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| A100098 |
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An inverse Chebyshev transform of (1-x)/(1-2x). |
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+0
3
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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, 284470564, 710118262, 1777323772, 4439253196, 11105933440, 27749232700, 69403169200
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Image of (1-x)/(1-2x) under the transform g(x)->(1/sqrt(1-4xx^2)g(xc(x^2)), where c(x) is the g.f. of the Catalan numbers A000108. This is the inverse of the Chebyshev transform which takes A(x) to ((1-x^2)/(1+x^2))A(x/(1+x^2).
Transform of the Jacobsthal numbers A001045(n+1) under the Riordan array (c(x^2),xc(x^2)). Hankel transform is 3^n. - Paul Barry (pbarry(AT)wit.ie), Oct 01 2007
Unsigned version of A127361 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 25 2007
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FORMULA
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G.f.: sqrt(1-4x^2)(sqrt(1-4x^2)-6x+3)/(2(2-5x)(1-4x^2)); a(n)=sum{k=0..floor(n/2), binomial(n, k)*(2^(n-2k)+0^(n-2k)/2}.
G.f.: (1+2x+3*sqrt(1-4x^2))/(4-2x-20x^2); a(n)=sum{k=0..floor((n+1)/2), (C(n,k)-C(n,k-1))*A001045(n-2k+1)}; - Paul Barry (pbarry(AT)wit.ie), Oct 01 2007
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CROSSREFS
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Adjacent sequences: A100095 A100096 A100097 this_sequence A100099 A100100 A100101
Sequence in context: A119561 A026548 A127361 this_sequence A128533 A126094 A073114
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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), Nov 04 2004
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