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A128213
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Expansion of (1-x+2x^2-2x^3)/(1-x+x^2)^2.
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1
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1, 1, 1, -1, -4, -4, 1, 7, 7, -1, -10, -10, 1, 13, 13, -1, -16, -16, 1, 19, 19, -1, -22, -22, 1, 25, 25, -1, -28, -28, 1, 31, 31, -1, -34, -34, 1, 37, 37, -1, -40, -40, 1, 43, 43, -1, -46, -46, 1, 49, 49, -1, -52, -52, 1, 55, 55, -1, -58, -58, 1, 61, 61, -1
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OFFSET
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0,5
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COMMENTS
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a(n+1) is the Hankel transform of {1,0,1,3,9,28,90,297,1001,3432,11934,...}, cf. A000245.
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LINKS
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FORMULA
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a(n) = cos(Pi*n/3) + (2n/sqrt(3)-1/sqrt(3))*sin(Pi*n/3).
a(n) = y(n,n), where y(m+1,n) = y(m,n) - y(m-1,n), with y(0,n)=1 and y(1,n)=n. - Benedict W. J. Irwin, Nov 05 2016
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MATHEMATICA
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Table[DifferenceRoot[Function[{y, m}, {y[1 + m] == y[m] - y[m - 1], y[0] == 1, y[1] == n}]][n], {n, 0, 100}] (* Benedict W. J. Irwin, Nov 05 2016 *)
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PROG
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(PARI) Vec((1-x+2*x^2-2*x^3)/(1-x+x^2)^2 + O(x^100)) \\ Michel Marcus, May 31 2014
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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