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Search: id:A115255
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| A115255 |
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"Correlation triangle" of central binomial coefficients A000984. |
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+0
3
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| 1, 2, 2, 6, 5, 6, 20, 14, 14, 20, 70, 46, 41, 46, 70, 252, 160, 134, 134, 160, 252, 924, 574, 466, 441, 466, 574, 924, 3432, 2100, 1672, 1534, 1534, 1672, 2100, 3432, 12870, 7788, 6118, 5506, 5341, 5506, 6118, 7788, 12870, 48620, 29172, 22692, 20152, 19174
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums are A033114. Diagonal sums are A115256. T(2n,n) is A115257. Corresponds to the triangle of antidiagonals of the correlation matrix of the sequence array for C(2n,n).
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FORMULA
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G.f.: 1/(sqrt(1-4x)*sqrt(1-4x*y)*(1-x^2*y)) (format due to Christian G. Bower); Number triangle T(n, k)=sum{j=0..n, [j<=k]*C(2k-2j, k-j)[j<=n-k]*C(2n-2k-2j, n-k-j)}.
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EXAMPLE
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Triangle begins
1;
2, 2;
6, 5, 6;
20, 14, 14, 20;
70, 46, 41, 46, 70;
252, 160, 134, 134, 160, 252;
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CROSSREFS
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Sequence in context: A019749 A122070 A144160 this_sequence A055924 A054917 A111419
Adjacent sequences: A115252 A115253 A115254 this_sequence A115256 A115257 A115258
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 18 2006
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