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A082578
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a(n) = Sum_{k=0..n} binomial(2*k, k) * binomial(2*k+1,k).
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3
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1, 7, 67, 767, 9587, 126011, 1711595, 23796515, 336666215, 4828084575, 69994481871, 1023793569567, 15086216016367, 223704570996367, 3335098322412367, 49954148031128767, 751296616443141667
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OFFSET
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0,2
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COMMENTS
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Old name was "A binomial sum".
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LINKS
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FORMULA
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Recurrence: (n+3)*(n+2)*a(n+2) - (17*n^2+69*n+66)*a(n+1) + (16*n^2+64*n+60)*a(n) = 0.
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MATHEMATICA
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Table[Sum[Binomial[2k, k]*Binomial[2k+1, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)
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PROG
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(Maxima) makelist(sum(binomial(2*k, k)*binomial(2*k+1, k), k, 0, n), n, 0, 12);
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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