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A128064
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A natural number transform.
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23
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1, -1, 2, 0, -2, 3, 0, 0, -3, 4, 0, 0, 0, -4, 5, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, -6, 7, 0, 0, 0, 0, 0, 0, -7, 8
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The matrix inverse = (1/1; 1/2, 1/2; 1/3, 1/3, 1/3;...). Binomial transform of A128064 = A128065 A128064 * A007318 = A103406
The positive version with row sums 2n+1 is given by T(n,k)=sum{j=k..n, C(n,j)*C(j,k)*(-1)^(n-j)*(j+1)}. - Paul Barry (pbarry(AT)wit.ie), May 26 2007
Binomial transform of unsigned sequence is A003506. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 29 2007
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FORMULA
| Triangle read by rows: row 1 = 1, row 2 = (-1, 2); (n-2) zeros followed by -(n-1), n. Infinite lower triangular matrix with (1, 2, 3,...) as the right border, (-1, -2, -3,...) as the adjacent diagonal and the rest zeros.
Number triangle T(n,k)=sum{j=k..n, C(n,j)*C(j,k)*(-1)^(j-k)*(j+1)} - Paul Barry (pbarry(AT)wit.ie), May 26 2007
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EXAMPLE
| First few rows of the triangle are:
1;
-1, 2;
0, -2, 3;
0, 0, -3, 4;
0, 0, 0, -4, 5;
...
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CROSSREFS
| Cf. A128065, A103406.
Cf. A003506.
Sequence in context: A053571 A129883 A098489 * A144217 A187881 A132814
Adjacent sequences: A128061 A128062 A128063 * A128065 A128066 A128067
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KEYWORD
| tabl,sign
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 14 2007
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