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A114117
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Inverse of 1's counting matrix A114116.
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2
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1, 0, 1, -2, 1, 1, -1, -1, 1, 1, 0, -2, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, 0, -2, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums are (1,1,0,0,0,.....) with g.f. 1+x. Diagonal sums have g.f. (1-x^2-x^3)/(1-x^3). Product of A114115 and the first difference matrix (1-x,x).
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FORMULA
| T(n, k)=sum{j=0..n, sum{i=0..n, C(floor((n+i)/2, j)C(j, floor((n+i)/2))}*(2*C(0, j-k)-C(1, j-k))}}.
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EXAMPLE
| Triangle begins
1;
0, 1;
-2, 1, 1;
-1,-1, 1, 1;
0,-2, 0, 1, 1;
0,-1,-1, 0, 1, 1;
0, 0,-2, 0, 0, 1, 1;
0, 0,-1,-1, 0, 0, 1, 1;
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CROSSREFS
| Sequence in context: A037910 A162781 A056975 * A144435 A173120 A025920
Adjacent sequences: A114114 A114115 A114116 * A114118 A114119 A114120
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KEYWORD
| easy,sign,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 13 2005
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