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A115179
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Expansion of c(x*y(1-x)), c(x) the g.f. of A000108.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| 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
| Number triangle T(n,k)=(-1)^(n-k)*C(k)*C(k,n-k).
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EXAMPLE
| 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
| Sequence in context: A094295 A085969 A117434 * A131742 A056676 A098699
Adjacent sequences: A115176 A115177 A115178 * A115180 A115181 A115182
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 14 2006
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