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A100099
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An inverse Chebyshev transform of x/(1-2x).
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0
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0, 1, 2, 7, 16, 46, 110, 295, 720, 1870, 4612, 11782, 29224, 73984, 184102, 463687, 1156000, 2902870, 7245020, 18161170, 45356736, 113576596, 283765132, 710118262, 1774619616, 4439253196, 11095532840, 27749232700, 69363052600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Image of x/(1-2x) under the transform g(x)->(1/sqrt(1-4x^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).
Hankel transform is A125905(n-1), the alternating sign version of A001353. - Paul Barry (pbarry(AT)wit.ie), Nov 25 2007
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FORMULA
| G.f.: sqrt(1-4x^2)(sqrt(1-4x^2)+4x-1)/(2(5x-2)(4x^2-1)); a(n)=sum{k=0..floor(n/2), binomial(n, k)*(2^(n-2k)-0^(n-2k)/2}.
a(n)=sum{k=0..n, C(n,floor(k/2))A001045(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Nov 25 2007
Conjecture: 2n*a(n) +(-13n+16)*a(n-1) +4(3n-8)*a(n-2) +4(13n-29)*a(n-3) +80(3-n)*a(n-4)=0. - R. J. Mathar, Dec 14 2011
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CROSSREFS
| Sequence in context: A113224 A178945 A026571 * A164267 A184352 A000512
Adjacent sequences: A100096 A100097 A100098 * A100100 A100101 A100102
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 04 2004
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