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Search: id:A099363
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| A099363 |
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An inverse Chebyshev transform of 1-x. |
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+0
3
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| 1, -1, 1, -2, 2, -5, 5, -14, 14, -42, 42, -132, 132, -429, 429, -1430, 1430, -4862, 4862, -16796, 16796, -58786, 58786, -208012, 208012, -742900, 742900, -2674440, 2674440, -9694845, 9694845, -35357670, 35357670, -129644790, 129644790, -477638700, 477638700, -1767263190, 1767263190
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Second binomial transform of the expansion of c(-x)^3. The g.f. is transformed to 1-x under the Chebyshev transformation A(x)->(1/(1+x^2))A(x/(1+x^2)).
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FORMULA
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G.f.: (1-(1-x)c(x^2))/x where c(x) is the g.f. of the Catalan numbers A000108; a(n)=sum{k=0..n, (k+1)C(n, (n-k)/2)(0^k-sum{j=0..k, C(k, j)(-1)^(k-j)*j})(1+(-1)^(n-k))/(n+k+2)}.
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CROSSREFS
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Cf. A000245.
Sequence in context: A056507 A095014 A129996 this_sequence A106181 A098887 A097438
Adjacent sequences: A099360 A099361 A099362 this_sequence A099364 A099365 A099366
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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), Oct 13 2004
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