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Search: id:A003583
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| A003583 |
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(n+2)*2^(2*n-1)-(n/2)*binomial(2*n,n). |
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+0
1
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| 1, 5, 26, 130, 628, 2954, 13612, 61716, 276200, 1223002, 5367676, 23383100, 101215576, 435712580, 1866667448, 7963424104, 33846062544, 143373104378, 605518549660, 2550438016812, 10716162617336
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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M. Hirschhorn, Calkin's binomial identity, Discr. Math., 159 (1996), 273-278.
Jun Wang and Zhizheng Zhang, On extensions of Calkin's binomial identities, Discrete Math., 274 (2004), 331-342.
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FORMULA
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Main diagonal of correlation matrix of A055248. a(n)=sum{k=0..n, (sum{m=k..n, binomial(n, m)})^2 } - Paul Barry (pbarry(AT)wit.ie), Jun 05 2003
Let S2 := (n, t)->add( k^t * (add( binomial(n, j), j=0..k))^2, k=0..n); a(n) = S2(n, 0).
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CROSSREFS
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Adjacent sequences: A003580 A003581 A003582 this_sequence A003584 A003585 A003586
Sequence in context: A047669 A002316 A005499 this_sequence A033115 A033123 A047770
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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