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A119580
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a(n) = (n^2+n^3)*binomial(2*n,n).
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0
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0, 4, 72, 720, 5600, 37800, 232848, 1345344, 7413120, 39382200, 203231600, 1024287264, 5062180032, 24607819600, 117942804000, 558423072000, 2615901857280, 12139419556440, 55866532906800, 255192804636000, 1157910842088000, 5222177897816880, 23422829664131040
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OFFSET
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0,2
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = Pi/sqrt(3) - Pi^2/18 - 1.
Sum_{n>=1} (-1)^(n+1)/a(n) = 6*log(phi)^2 - 2*sqrt(5)*log(phi) + 1, where phi is the golden ratio (A001622). (End)
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MAPLE
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[seq ((n^2+n^3)*(binomial(2*n, n)), n=0..29)];
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MATHEMATICA
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Table[(n^2 + n^3) * Binomial[2 n, n], {n, 0, 30}] (* Wesley Ivan Hurt, Feb 26 2014 *)
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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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STATUS
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approved
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