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Search: id:A115179
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| 1, 0, 1, 0, -1, 2, 0, 0, -4, 5, 0, 0, 2, -15, 14, 0, 0, 0, 15, -56, 42, 0, 0, 0, -5, 84, -210, 132, 0, 0, 0, 0, -56, 420, -792, 429, 0, 0, 0, 0, 14, -420, 1980, -3003, 1430, 0, 0, 0, 0, 0, 210, -2640, 9009, -11440, 4862, 0, 0, 0, 0, 0, -42, 1980, -15015, 40040, -43758, 16796, 0, 0, 0, 0, 0, 0, -792
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Since c(x(1-x))=1/(1-x), the row sums of this triangle are (1,1,1,...). This establishes the identity sum{k=0..n, (-1)^(n-k)*C(k)*C(k,n-k)}=1. Diagonal sums are A117437. Alternating sign version of A117434.
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FORMULA
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Number triangle T(n,k)=(-1)^(n-k)*C(k)*C(k,n-k).
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EXAMPLE
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Triangle begins
1,
0, 1,
0, -1, 2,
0, 0, -4, 5,
0, 0, 2, -15, 14,
0, 0, 0, 15, -56, 42,
0, 0, 0, -5, 84, -210, 132,
0, 0, 0, 0, -56, 420, -792, 429
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CROSSREFS
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Sequence in context: A094295 A085969 A117434 this_sequence A131742 A056676 A098699
Adjacent sequences: A115176 A115177 A115178 this_sequence A115180 A115181 A115182
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 14 2006
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