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Search: id:A047171
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| A047171 |
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Number of nonempty subsets of {1,2,...,n} in which exactly 1/2 of the elements are <= (n-1)/2. |
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+0
2
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| 0, 0, 2, 3, 9, 14, 34, 55, 125, 209, 461, 791, 1715, 3002, 6434, 11439, 24309, 43757, 92377, 167959, 352715, 646645, 1352077, 2496143, 5200299, 9657699, 20058299, 37442159, 77558759, 145422674, 300540194, 565722719, 1166803109
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OFFSET
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1,3
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FORMULA
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a(n) = A037952(n) - 1. Proof by Ira Gessel: Write down the number of such subsets with k elements <= (n-1)/2 as a product of two binomial coefficients, then evaluate the sum using Vandermonde's theorem.
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CROSSREFS
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Sequence in context: A113501 A101067 A056645 this_sequence A094557 A026307 A139816
Adjacent sequences: A047168 A047169 A047170 this_sequence A047172 A047173 A047174
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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