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A373164
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Triangle read by rows: the exponential almost-Riordan array ( 1 | 2 - exp(x), x ).
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0
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1, 0, 1, 0, -1, 1, 0, -1, -2, 1, 0, -1, -3, -3, 1, 0, -1, -4, -6, -4, 1, 0, -1, -5, -10, -10, -5, 1, 0, -1, -6, -15, -20, -15, -6, 1, 0, -1, -7, -21, -35, -35, -21, -7, 1, 0, -1, -8, -28, -56, -70, -56, -28, -8, 1, 0, -1, -9, -36, -84, -126, -126, -84, -36, -9, 1
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OFFSET
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0,9
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LINKS
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FORMULA
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T(n,0) = A000007(n); T(n,k) = (n-1)!/(k-1)! * [x^(n-1)] (2-exp(x))*x^(k-1).
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EXAMPLE
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The triangle begins:
1;
0, 1;
0, -1, 1;
0, -1, -2, 1;
0, -1, -3, -3, 1;
0, -1, -4, -6, -4, 1;
0, -1, -5, -10, -10, -5, 1;
0, -1, -6, -15, -20, -15, -6, 1;
0, -1, -7, -21, -35, -35, -21, -7, 1;
...
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MATHEMATICA
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T[n_, 0]:=KroneckerDelta[n, 0]; T[n_, k_]:=(n-1)!/(k-1)!SeriesCoefficient[(2-Exp[x])x^(k-1), {x, 0, n-1}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
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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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