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Search: id:A115253
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| A115253 |
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"Correlation triangle" for Catalan numbers. |
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+0
3
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| 1, 1, 1, 2, 2, 2, 5, 3, 3, 5, 14, 7, 6, 7, 14, 42, 19, 13, 13, 19, 42, 132, 56, 35, 31, 35, 56, 132, 429, 174, 103, 83, 83, 103, 174, 429, 1430, 561, 320, 245, 227, 245, 320, 561, 1430, 4862, 1859, 1032, 763, 671, 671, 763, 1032, 1859, 4862, 16796, 6292, 3421
(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 A094639. Diagonal sums are A115254. Corresponds to the triangle of antidiagonals of the correlation matrix of the sequence array for C(n).
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FORMULA
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G.f.: c(x)c(x*y)/(1-x^2*y) where c(x) is the g.f. of A000108 (format due to Christian G. Bower); Number triangle T(n, k)=sum{j=0..n, [j<=k]*C(k-j)[j<=n-k]*C(n-k-j)}.
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EXAMPLE
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Triangle begins
1;
1, 1;
2, 2, 2;
5, 2, 2, 5;
14, 7, 6, 7, 14;
42, 19, 13, 13, 19, 42;
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CROSSREFS
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Sequence in context: A069862 A075002 A061311 this_sequence A076737 A134634 A103286
Adjacent sequences: A115250 A115251 A115252 this_sequence A115254 A115255 A115256
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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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