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A129368
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a(n) = Sum_{k=floor((n+1)/2)..n} binomial(2*k,k).
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2
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1, 2, 8, 26, 96, 342, 1266, 4678, 17548, 66098, 250854, 956034, 3660190, 14059866, 54176466, 209290554, 810370944, 3143964294, 12219099594, 47564314774, 185410843594, 723668533278, 2827767496998, 11061197519166
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1/(1-x))*( 1/sqrt(1-4*x) - x/sqrt(1-4*x^2) ).
a(n) = Sum_{k=0..floor(n/2)} C(2*(n-k), n-k).
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MATHEMATICA
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Table[Sum[Binomial[2k, k], {k, Floor[(n+1)/2], n}], {n, 0, 30}] (* Harvey P. Dale, Aug 13 2012 *)
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PROG
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(Magma) [(&+[Binomial(2*(n-k), n-k): k in [0..Floor(n/2)]]): n in [0..60]]; // G. C. Greubel, Jan 31 2024
(SageMath) [sum(binomial(2*(n-k), n-k) for k in range(1+(n//2))) for n in range(61)] # G. C. Greubel, Jan 31 2024
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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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