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A052473
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a(n) = binomial(2*n-5,n-2) + 2.
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2
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2, 2, 3, 3, 5, 12, 37, 128, 464, 1718, 6437, 24312, 92380, 352718, 1352080, 5200302, 20058302, 77558762, 300540197, 1166803112, 4537567652, 17672631902, 68923264412, 269128937222, 1052049481862, 4116715363802, 16123801841552
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OFFSET
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0,1
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COMMENTS
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The best upper bound known for the Erdős-Szekeres problem for n >= 6.
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LINKS
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FORMULA
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a(n) = 2 + (2^(2*n-5)*Gamma(n - 3/2))/(sqrt(Pi)*Gamma(n-1)).
G.f.: (x^2*(1-x) + (4 + x^2 -x^3)*sqrt(1-4*x))/(2*(1-x)*sqrt(1-4*x)). - Eric W. Weisstein, Jul 29 2011
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MAPLE
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seq( binomial(2*n-5, n-2) + 2, n=0..40); # Robert Israel, May 19 2019
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MATHEMATICA
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Table[Binomial[2n-5, n-2] + 2, {n, 0, 30}]
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PROG
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(Magma) [2 +Binomial(2*n-5, n-2): n in [0..30]]; // G. C. Greubel, May 18 2019
(Sage) [2 +binomial(2*n-5, n-2) for n in (0..30)] # G. C. Greubel, May 18 2019
(GAP) List([0..30], n-> 2+Binomial(2*n-5, n-2)) # G. C. Greubel, May 18 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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