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A112465
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Riordan array (1/(1+x),x/(1-x)).
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2
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1, -1, 1, 1, 0, 1, -1, 1, 1, 1, 1, 0, 2, 2, 1, -1, 1, 2, 4, 3, 1, 1, 0, 3, 6, 7, 4, 1, -1, 1, 3, 9, 13, 11, 5, 1, 1, 0, 4, 12, 22, 24, 16, 6, 1, -1, 1, 4, 16, 34, 46, 40, 22, 7, 1, 1, 0, 5, 20, 50, 80, 86, 62, 29, 8, 1, -1, 1, 5, 25, 70, 130, 166, 148, 91, 37, 9, 1, 1, 0, 6, 30, 95, 200, 296, 314, 239, 128, 46, 10, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| Row sums are A078008. Diagonal sums are A078024. Inverse is A112466. Note that C(n,k)=sum{j=0..n-k, C(j+k-1,j)}.
Central coefficients T(2n,n) are A072547. [Paul Barry, April 8 2011]
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REFERENCES
| E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Mathematics, 34 (2005) pp. 101-122.
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FORMULA
| Number triangle T(n, k)=sum{j=0..n-k, C(j+k-1, j)*(-1)^(n-k-j)}
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EXAMPLE
| Triangle starts
1;
-1,1;
1,0,1;
-1,1,1,1;
1,0,2,2,1;
-1,1,2,4,3,1;
1,0,3,6,7,4,1;
Production matrix begins
-1, 1,
0, 1, 1,
0, 0, 1, 1,
0, 0, 0, 1, 1,
0, 0, 0, 0, 1, 1,
0, 0, 0, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 1, 1,
0, 0, 0, 0, 0, 0, 0, 1, 1
[Paul Barry, April 8 2011]
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CROSSREFS
| Cf. A112468, A059260.
Sequence in context: A031282 A085685 * A112468 A086275 A066855 A175685
Adjacent sequences: A112462 A112463 A112464 * A112466 A112467 A112468
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 06 2005
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