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Search: id:A109466
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| A109466 |
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Riordan array (1, x(1-x)). |
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+0
8
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| 1, 0, 1, 0, -1, 1, 0, 0, -2, 1, 0, 0, 1, -3, 1, 0, 0, 0, 3, -4, 1, 0, 0, 0, -1, 6, -5, 1, 0, 0, 0, 0, -4, 10, -6, 1, 0, 0, 0, 0, 1, -10, 15, -7, 1, 0, 0, 0, 0, 0, 5, -20, 21, -8, 1, 0, 0, 0, 0, 0, -1, 15, -35, 28, -9, 1, 0, 0, 0, 0, 0, 0, -6, 35, -56, 36, -10, 1, 0, 0, 0, 0, 0, 0, 1, -21, 70, -84, 45, -11, 1, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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Inverse is Riordan array (1, xc(x)) (A106566).
Triangle T(n,k), 0<=k<=n, read by rows, given by [0, -1, 1, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
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FORMULA
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Number triangle T(n, k) = (-1)^(n-k)*binomial(k, n-k).
T(n, k)*2^(n-k) = A110509(n, k); T(n, k)*3^(n-k) = A110517(n, k).
Sum_{k, 0<=k<=n}T(n,k)*A000108(k)=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 11 2007
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EXAMPLE
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Rows begin:
1;
0, 1;
0, -1, 1;
0, 0, -2, 1;
0, 0, 1, -3, 1;
0, 0, 0, 3, -4, 1;
0, 0, 0, -1, 6, -5, 1;
0, 0, 0, 0, -4, 10, -6, 1;
0, 0, 0, 0, 1, -10, 15, -7, 1;
0, 0, 0, 0, 0, 5, -20, 21, -8, 1;
0, 0, 0, 0, 0, -1, 15, -35, 28, -9, 1;
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CROSSREFS
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Cf. : A026729 (unsigned version).
Adjacent sequences: A109463 A109464 A109465 this_sequence A109467 A109468 A109469
Sequence in context: A061670 A108063 A026729 this_sequence A076833 A071676 A115363
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 28 2005
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