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Search: id:A114117
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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; listen)
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OFFSET
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0,4
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COMMENT
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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
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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
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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
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Sequence in context: A076493 A037910 A056975 this_sequence A144435 A025920 A037821
Adjacent sequences: A114114 A114115 A114116 this_sequence A114118 A114119 A114120
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 13 2005
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