%I A047171
%S A047171 0,0,2,3,9,14,34,55,125,209,461,791,1715,3002,6434,11439,24309,43757,
%T A047171 92377,167959,352715,646645,1352077,2496143,5200299,9657699,20058299,
%U A047171 37442159,77558759,145422674,300540194,565722719,1166803109
%N A047171 Number of nonempty subsets of {1,2,...,n} in which exactly 1/2 of the 
               elements are <= (n-1)/2.
%F A047171 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.
%Y A047171 Sequence in context: A113501 A101067 A056645 this_sequence A094557 A026307 
               A139816
%Y A047171 Adjacent sequences: A047168 A047169 A047170 this_sequence A047172 A047173 
               A047174
%K A047171 nonn
%O A047171 1,3
%A A047171 Clark Kimberling (ck6(AT)evansville.edu)