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A091698
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Matrix inverse of triangle A063967.
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4
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1, -1, 1, 1, -3, 1, -1, 8, -5, 1, 1, -23, 19, -7, 1, -1, 74, -69, 34, -9, 1, 1, -262, 256, -147, 53, -11, 1, -1, 993, -986, 615, -265, 76, -13, 1, 1, -3943, 3935, -2571, 1235, -431, 103, -15, 1, -1, 16178, -16169, 10862, -5591, 2216, -653, 134, -17, 1, 1
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graph;
refs;
listen;
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text;
internal format)
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OFFSET
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0,5
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COMMENTS
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Riordan array (1/(1+x), (sqrt(1+6x+5x^2)-x-1)/(2(1+x))). The absolute value array is (1/(1-x),xc(x)/(1-xc(x))) where c(x) is the g.f. of A000108. It factorizes as (1/(1-x),x/(1-x))(1,xc(x)). - Paul Barry, Jun 10 2005
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LINKS
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EXAMPLE
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Triangle begins
1,
-1, 1,
1, -3, 1,
-1, 8, -5, 1,
1, -23, 19, -7, 1,
-1, 74, -69, 34, -9, 1,
1, -262, 256, -147, 53, -11, 1,
-1, 993, -986, 615, -265, 76, -13, 1,
1, -3943, 3935, -2571, 1235, -431, 103, -15, 1
Production matrix begins
-1, 1,
0, -2, 1,
0, 1, -2, 1,
0, -1, 1, -2, 1,
0, 1, -1, 1, -2, 1,
0, -1, 1, -1, 1, -2, 1,
0, 1, -1, 1, -1, 1, -2, 1,
0, -1, 1, -1, 1, -1, 1, -2, 1,
0, 1, -1, 1, -1, 1, -1, 1, -2, 1,
0, -1, 1, -1, 1, -1, 1, -1, 1, -2, 1 (End)
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MATHEMATICA
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rows = 11; t[n_, k_] := Sum[Binomial[j, n - j]*Binomial[j, k], {j, 0, n}]; T = Table[t[n, k], {n, 0, rows - 1}, {k, 0, rows - 1}] // Inverse; Table[ T[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 11 2017 *)
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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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