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A047171 Number of nonempty subsets of {1,2,...,n} in which exactly 1/2 of the elements are <= (n-1)/2. 1
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 (list; graph; refs; listen; history; internal format)
OFFSET

1,3

FORMULA

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.

CROSSREFS

Sequence in context: A113501 A101067 A056645 * A094557 A026307 A139816

Adjacent sequences:  A047168 A047169 A047170 * A047172 A047173 A047174

KEYWORD

nonn

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu)

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Last modified February 14 23:53 EST 2012. Contains 205689 sequences.