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A078996
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Triangle read by rows: let f(x) = x/(1-x-x^2); n-th row gives coefficients of denominator polynomial of n-th derivative f(x)^(n), with highest powers first, for n >= 0.
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0
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-1, -1, 1, 1, 2, -1, -2, 1, 1, 3, 0, -5, 0, 3, -1, 1, 4, 2, -8, -5, 8, 2, -4, 1, 1, 5, 5, -10, -15, 11, 15, -10, -5, 5, -1, 1, 6, 9, -10, -30, 6, 41, -6, -30, 10, 9, -6, 1, 1, 7, 14, -7, -49, -14, 77, 29, -77, -14, 49, -7, -14, 7, -1, 1, 8, 20, 0, -70, -56, 112, 120, -125, -120, 112, 56, -70, 0, 20, -8, 1
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OFFSET
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0,5
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LINKS
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FORMULA
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f(x)^(n), for n=0, 1, 2, 3, 4, ..., where f(x)= x/(1-x-x^2).
G.f.: G(0)/(2*x) - 1/x - 2 - 2*x + 2*x^2 , where G(k)= 1 + 1/( 1 - (1+x-x^2)*x^(2*k+1)/((1+x-x^2)*x^(2*k+1) + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 06 2013
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EXAMPLE
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Triangle begins:
-1, -1, 1;
1, 2, -1, -2, 1;
1, 3, 0, -5, 0, 3, -1;
...
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CROSSREFS
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See A084610 for another version of this triangle.
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KEYWORD
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sign,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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