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A047161
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Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= n/2.
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6
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0, 0, 1, 2, 6, 9, 21, 30, 70, 100, 235, 335, 791, 1127, 2681, 3822, 9150, 13050, 31401, 44802, 108262, 154517, 374715, 534963, 1301235, 1858155, 4531423, 6472167, 15818791, 22597759, 55339849, 79067374, 193962894, 277164294, 680963509, 973184312, 2394289028, 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), k)*binomial(ceiling(n/2), 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+1)\4, binomial(m, k)*binomial(n-m, 2*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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