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A068554
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a(n) = n*binomial(2n, n) - 4^n.
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1
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-1, -2, -4, -4, 24, 236, 1448, 7640, 37424, 175436, 798984, 3565448, 15672656, 68098936, 293196944, 1253020976, 5322318944, 22491436556, 94632958664, 396682105256, 1657418948624, 6905368852136, 28697991157424, 119000162557136
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OFFSET
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0,2
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COMMENTS
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Known to be >= 0 for n>3.
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REFERENCES
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Hojoo Lee, Posting to Number Theory List, Feb 18 2002.
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LINKS
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FORMULA
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G.f.: (2*x-sqrt(1-4*x))/(1-4*x)^(3/2).
a(n) = ((16*(n-2))*(2*n-5)*a(n-3)-(4*(8*n^2-23*n+18))*a(n-2)+(2*(5*n-4))*(n-1)*a(n-1))/(n*(n-1)). (End)
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MAPLE
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seq(n*binomial(2*n, n)-4^n, n=0..40); # Robert Israel, Nov 13 2016
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MATHEMATICA
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Table[n*Binomial[2n, n]-4^n, {n, 0, 30}] (* Harvey P. Dale, Nov 17 2012 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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