A069954 revision #21
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A069954
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a(n) = binomial(2^(n+1), 2^n)/2 = binomial(2^(n+1) - 1, 2^n) = binomial(2^(n+1) - 1, 2^n-1).
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3
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OFFSET
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0,2
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COMMENTS
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C(2*k, k)/2 = C(2*k-1, k) = C(2*k-1, k-1) is odd if and only if k = 2^n. - Michael Somos, Mar 12 2014
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LINKS
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FORMULA
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EXAMPLE
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C(2,1)/2 = C(1,0) = C(1,1) = 1. C(4,2)/2 = C(3,1) = C(3,2) = 3. C(8,4)/2 = C(7,3) = C(7,4) = 35. - Michael Somos, Mar 12 2014
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MATHEMATICA
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PROG
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(Magma) [Binomial(2^(n+1)-1, 2^n-1): n in [0..10]]; // Vincenzo Librandi, Mar 14 2014
(SageMath) [binomial(2^(n+1) -1, 2^n) for n in (0..9)] # G. C. Greubel, Aug 16 2022
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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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editing
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