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Floor of the expected number of empty cells in a random placement of 2n balls into n cells.
8

%I #12 Aug 03 2014 14:01:40

%S 0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,4,4,4,4,

%T 4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,9,

%U 9,9,9,9,9,9,10,10,10,10,10,10,10,10,11,11

%N Floor of the expected number of empty cells in a random placement of 2n balls into n cells.

%D W. Feller, An Introduction to Probability Theory and its Applications, 2nd ed, Wiley, New York, 1965, p. 226.

%F a(n) = floor(n*(1-1/n)^(2n)).

%t Table[Floor[n*(1 - 1/n)^(2 n)], {n, 100}] (* _T. D. Noe_, Mar 15 2012 *)

%Y Cf. A209900.

%K nonn

%O 1,16

%A _Washington Bomfim_, Mar 14 2012