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A110509
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Riordan array (1, x(1-2x)).
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7
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1, 0, 1, 0, -2, 1, 0, 0, -4, 1, 0, 0, 4, -6, 1, 0, 0, 0, 12, -8, 1, 0, 0, 0, -8, 24, -10, 1, 0, 0, 0, 0, -32, 40, -12, 1, 0, 0, 0, 0, 16, -80, 60, -14, 1, 0, 0, 0, 0, 0, 80, -160, 84, -16, 1, 0, 0, 0, 0, 0, -32, 240, -280, 112, -18, 1, 0, 0, 0, 0, 0, 0, -192, 560, -448, 144, -20, 1, 0, 0, 0, 0, 0, 0, 64, -672, 1120, -672, 180, -22, 1
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OFFSET
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0,5
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COMMENTS
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Inverse is Riordan array (1,xc(2x)) [A110510]. Row sums are A107920(n+1). Diagonal sums are (-1)^n*A052947(n).
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LINKS
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FORMULA
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Number triangle: T(n, k) = (-2)^(n-k)*binomial(k, n-k).
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EXAMPLE
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Rows begin
1;
0, 1;
0, -2, 1;
0, 0, -4, 1;
0, 0, 4, -6, 1;
0, 0, 0, 12, -8, 1;
0, 0, 0, -8, 24, -10, 1;
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MATHEMATICA
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T[n_, k_] := (-2)^(n - k)*Binomial[k, n - k]; Table[T[n, k], {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 29 2017 *)
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PROG
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(PARI) for(n=0, 25, for(k=0, n, print1((-2)^(n-k)*binomial(k, n-k), ", "))) \\ G. C. Greubel, Aug 29 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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