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A047162
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Number of nonempty subsets of {1,2,...,n} in which exactly 2/3 of the elements are <= n/2.
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3
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0, 0, 0, 2, 3, 9, 12, 30, 40, 100, 135, 335, 455, 1127, 1540, 3822, 5250, 13050, 18000, 44802, 62007, 154517, 214467, 534963, 744315, 1858155, 2590679, 6472167, 9039823, 22597759, 31612324, 79067374, 110761494, 277164294, 388742706, 973184312, 1366460867, 3422117189
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OFFSET
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1,4
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LINKS
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FORMULA
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a(n) = Sum_{k>=1} binomial(floor(n/2), 2*k)*binomial(ceiling(n/2), k). - Andrew Howroyd, Apr 11 2021
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PROG
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(PARI) a(n) = {my(m=n\2); sum(k=1, n\4, binomial(m, 2*k)*binomial(n-m, k))} \\ Andrew Howroyd, Apr 11 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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