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A014495
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Central binomial coefficient - 1.
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14
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0, 0, 1, 2, 5, 9, 19, 34, 69, 125, 251, 461, 923, 1715, 3431, 6434, 12869, 24309, 48619, 92377, 184755, 352715, 705431, 1352077, 2704155, 5200299, 10400599, 20058299, 40116599, 77558759, 155117519, 300540194, 601080389, 1166803109, 2333606219, 4537567649
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OFFSET
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0,4
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COMMENTS
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Number of Young tableaux with n cells and 2 rows. Also number of self-inverse permutations in S_n with longest increasing subsequence of length 2. The a(4) = 5 permutations are 1432, 2143, 3214, 3412, 4231 and the a(5) = 9 permutations are 15432, 21543, 32154, 35142, 42513, 43215, 45312, 52431, 53241. - Alois P. Heinz, Oct 03 2012
Number of nonempty subsets of {1,2,...,n} that contain the same number of even and odd numbers. For example, a(5)=9 and the 9 subsets are {1,2}, {1,4}, {2,3}, {2,5}, {3,4}, {4,5}, {1,2,3,4}, {1,2,4,5}, {2,3,4,5}. - Enrique Navarrete, Feb 10 2018
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LINKS
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FORMULA
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n*a(n)-2*a(n-1)-4*(n-2)*a(n-2) = 3*n-6 with n>1, a(0)=a(1)=0. - Bruno Berselli, Oct 03 2012
D-finite with recurrence: -(n+1)*(n-2)*a(n) +(n^2+n-4)*a(n-1) +2*(n-1)*(2*n-5)*a(n-2) -4*(n-1)*(n-2)*a(n-3)=0. - Conjectured by R. J. Mathar, Jan 04 2017, confirmed by Robert Israel, Feb 11 2018
G.f.: (x+1)/(2*x*(x-1)) - sqrt(1-4*x^2)/(2*x*(2*x-1)). - Robert Israel, Feb 11 2018
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MAPLE
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a:= n-> binomial(n, iquo(n, 2))-1:
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MATHEMATICA
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Table[Binomial[n - 1, Floor[(n - 1)/2]] - 1, {n, 0, 50}] (* Bruno Berselli, Oct 03 2012 *)
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PROG
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(Maxima) A014495(n):=binomial(n-1, floor((n-1)/2))-1$
(Magma) [Binomial(n-1, Floor((n-1)/2))-1: n in [1..50]]; // Vincenzo Librandi, Feb 11 2018
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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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