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A117179
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Riordan array ((1-x^2)/(1+x^2)^2,x/(1+x^2)).
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2
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1, 0, 1, -3, 0, 1, 0, -4, 0, 1, 5, 0, -5, 0, 1, 0, 9, 0, -6, 0, 1, -7, 0, 14, 0, -7, 0, 1, 0, -16, 0, 20, 0, -8, 0, 1, 9, 0, -30, 0, 27, 0, -9, 0, 1, 0, 25, 0, -50, 0, 35, 0, -10, 0, 1, -11, 0, 55, 0, -77, 0, 44, 0, -11, 0, 1
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OFFSET
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0,4
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COMMENTS
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Inverse is A117178. Row sums are (-1)^n*A098554(n+1). Diagonal sums are 1,0,-2,0,2,0,-2,... with g.f. (1-x^2)/(1+x^2).
Apparently, with the rows de-aerated and then reversed, this matrix becomes signed A034807 with the twos on the diagonal removed. Apparently, |D(2n,k+1)| = |D(2(n-1),k+1)| + |D(2n,k)| where D(n,k) is the k-th element on the n-th diagonal. - Tom Copeland, May 30 2017
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LINKS
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EXAMPLE
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Triangle begins
1,
0, 1,
-3, 0, 1,
0, -4, 0, 1,
5, 0, -5, 0, 1,
0, 9, 0, -6, 0, 1,
-7, 0, 14, 0, -7, 0, 1,
0, -16, 0, 20, 0, -8, 0, 1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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