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A119337
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Number triangle T(n,k)=sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,3j)*C(i-k,3j)}}.
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1
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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, -9, 10, -5, 1, 0, 1, -6, 12, -16, 15, -6, 1, 0, -1, 7, -15, 19, -25, 21, -7, 1, 0, 1, -8, 18, -16, 20, -36, 28, -8, 1, 0, -1, 9, -21, 4, 24, 6, -49, 36, -9, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Row sums have g.f. (1+x)/(1-x)^6. Multiply by Pascal's triangle A007318 to get A119335.
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FORMULA
| Column k has g.f. (x/(1+x))^k*sum{j=0..k, C(k,3j)x^(3j)}
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EXAMPLE
| 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, -9, 10, -5, 1,
0, 1, -6, 12, -16, 15, -6, 1,
0, -1, 7, -15, 19, -25, 21, -7, 1,
0, 1, -8, 18, -16, 20, -36, 28, -8, 1,
0, -1, 9, -21, 4, 24, 6, -49, 36, -9, 1
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CROSSREFS
| Sequence in context: A121480 A082601 A077593 * A110555 A071919 A097805
Adjacent sequences: A119334 A119335 A119336 * A119338 A119339 A119340
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 14 2006
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