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A047163
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Number of nonempty subsets of {1,2,...,n} in which exactly 1/4 of the elements are <= n/2.
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2
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0, 0, 0, 0, 2, 3, 12, 16, 40, 50, 110, 135, 315, 392, 980, 1232, 3080, 3864, 9480, 11850, 29040, 36300, 89870, 112519, 280423, 351351, 876603, 1098188, 2741102, 3433703, 8586788, 10758608, 26965808, 33794504, 84844280, 106344792, 267298650, 335061789, 843098172, 1056924666
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OFFSET
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1,5
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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), 3*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-m)\3, binomial(m, k)*binomial(n-m, 3*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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