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Search: id:A129763
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| A129763 |
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Sum[ Binomial[ n+k-1, n ]^2, {k,1,n} ] / n. |
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+0
1
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| 1, 5, 39, 369, 3898, 44239, 528083, 6544745, 83496720, 1090091650, 14501708246, 195954553755, 2682953977174, 37150480629539, 519455719162283, 7325383709872345, 104080732316126716, 1488685017986884528
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OFFSET
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1,2
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COMMENT
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Note that Sum[ Binomial[ n+k-1, n ], {k,1,n} ] / n = Catalan(n) = A000108(n).
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FORMULA
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a(n) = Sum[ Binomial[ n+k-1, n ]^2, {k,1,n} ] / n.
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MATHEMATICA
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Table[ Sum[ Binomial[ n+k-1, n ]^2, {k, 1, n} ] / n, {n, 1, 30} ]
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CROSSREFS
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Cf. A000108 = Catalan numbers.
Sequence in context: A135849 A105426 A115187 this_sequence A070767 A124549 A024216
Adjacent sequences: A129760 A129761 A129762 this_sequence A129764 A129765 A129766
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), May 15 2007
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