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A058621
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a(n) = 1/2*binomial(2*n,n) - (1+(-1)^n)/4*(binomial(n,floor(n/2)))^2.
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0
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0, 1, 1, 10, 17, 126, 262, 1716, 3985, 24310, 60626, 352716, 925190, 5200300, 14168988, 77558760, 217721745, 1166803110, 3355615450, 17672631900, 51855874642, 269128937220, 803232328548, 4116715363800, 12467572005382, 63205303218876, 193873026294052
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OFFSET
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0,4
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REFERENCES
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A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992.
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LINKS
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FORMULA
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a(n) = Sum_{i=0..(n-1)/2} binomial(n,i)^2 (see Equation 2 in section 4.2.5 of Prudnikov et al. reference).
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MATHEMATICA
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Table[1/2 * Binomial[2 n, n] - (1 + (-1)^n)/4 (Binomial[n, n/2])^2, {n, 0, 26}] (* Michael De Vlieger, Aug 25 2015 *)
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PROG
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(PARI) a(n) = 1/2*binomial(2*n, n) - (1+(-1)^n)/4*(binomial(n, n\2))^2;
(Magma) [1/2*Binomial(2*n, n)-(1+(-1)^n)/4*(Binomial(n, Floor(n/2)))^2: n in [0..30]]; // Vincenzo Librandi, Aug 25 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Yong Kong (ykong(AT)curagen.com), Dec 26 2000
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EXTENSIONS
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STATUS
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approved
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