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Search: id:A122908
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| A122908 |
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A central binomial scaling of the Riordan array (1+x,x) (A097806). |
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+0
1
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| 1, 1, 1, 0, 1, 2, 0, 0, 2, 3, 0, 0, 0, 3, 6, 0, 0, 0, 0, 6, 10, 0, 0, 0, 0, 0, 10, 20, 0, 0, 0, 0, 0, 0, 20, 35, 0, 0, 0, 0, 0, 0, 0, 35, 70, 0, 0, 0, 0, 0, 0, 0, 0, 70, 126, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 252
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Row sums are A050168. Diagonal sums are A001045 doubled. Row sums of inverse are 1/C(2n,n) aerated. Applications to other sequences are obvious.
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FORMULA
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Number triangle T(n,k)=C(k,floor(k/2))*sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)}
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EXAMPLE
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Triangle begins
.1,
.1, 1,
.0, 1, 2,
.0, 0, 2, 3,
.0, 0, 0, 3, 6,
.0, 0, 0, 0, 6, 10,
.0, 0, 0, 0, 0, 10, 20,
.0, 0, 0, 0, 0, 0, 20, 35,
.0, 0, 0, 0, 0, 0, 0, 35, 70,
.0, 0, 0, 0, 0, 0, 0, 0, 70, 126,
.0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 252
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CROSSREFS
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Sequence in context: A087611 A153869 A128541 this_sequence A091008 A111006 A046742
Adjacent sequences: A122905 A122906 A122907 this_sequence A122909 A122910 A122911
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 18 2006
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