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A101496
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Expansion of (1-x^2)/(1-x-x^2+x^3+x^4).
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0
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1, 1, 1, 1, 0, -1, -3, -5, -7, -8, -7, -3, 5, 17, 32, 47, 57, 55, 33, -16, -95, -199, -311, -399, -416, -305, -11, 499, 1209, 2024, 2745, 3061, 2573, 865, -2368, -7137, -12943, -18577, -22015, -20512, -11007, 9073, 40593, 81185, 123712, 155231, 157165, 107499, -14279, -219176
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OFFSET
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0,7
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COMMENTS
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Results from applying a Chebyshev transform after an inverse Catalan transform to 1/(1-x). The inverse Catalan transform maps g(x)->g(x(1-x)) while the Chebyshev transform maps h(x)->(1/(1+x^2))h(x/(1+x^2)).
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LINKS
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Table of n, a(n) for n=0..49.
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FORMULA
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a(n)=a(n-1)+a(n-2)-a(n-3)-a(n-4); a(n)=sum{k=0..floor(n/2), sum{j=0..floor((n-2k)/2), C(n-k, k)C(n-2k-j, j)}}.
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MATHEMATICA
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CoefficientList[Series[(1-x^2)/(1-x-x^2+x^3+x^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 1, -1, -1}, {1, 1, 1, 1}, 50] (* Harvey P. Dale, Jun 05 2012 *)
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CROSSREFS
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Sequence in context: A142340 A185168 A131979 * A218490 A161696 A196084
Adjacent sequences: A101493 A101494 A101495 * A101497 A101498 A101499
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry, Dec 04 2004
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STATUS
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approved
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