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Search: id:A124304
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| A124304 |
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Riordan array (1,x(1-x^2)). |
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+0
2
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| 1, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, -2, 0, 1, 0, 0, 0, -3, 0, 1, 0, 0, 1, 0, -4, 0, 1, 0, 0, 0, 3, 0, -5, 0, 1, 0, 0, 0, 0, 6, 0, -6, 0, 1, 0, 0, 0, -1, 0, 10, 0, -7, 0, 1, 0, 0, 0, 0, -4, 0, 15
(list; table; graph; listen)
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OFFSET
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0,13
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COMMENT
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Row sums are A050935(n+2). Diagonal sums are A014021. T(2n,n) is a signed aerated version of C(2n,n). Inverse is A124305.
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FORMULA
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Number triangle T(n,k):=sum{j=0..n, C(k,k-j)C(k,n-k-j)*(-1)^j}; T(n,k)=C(k,(n-k)/2))*(-1)^((n-k)/2)*(1+(-1)^(n-k))/2;
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EXAMPLE
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Triangle begins
1,
0, 1,
0, 0, 1,
0, -1, 0, 1,
0, 0, -2, 0, 1,
0, 0, 0, -3, 0, 1,
0, 0, 1, 0, -4, 0, 1,
0, 0, 0, 3, 0, -5, 0, 1,
0, 0, 0, 0, 6, 0, -6, 0, 1
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CROSSREFS
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Sequence in context: A091393 A110270 A123635 this_sequence A089812 A133988 A123858
Adjacent sequences: A124301 A124302 A124303 this_sequence A124305 A124306 A124307
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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), Oct 25 2006
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