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A210112 Floor of the expected value of number of trials until exactly one cell is empty in a random distribution of n balls in n cells. 5

%I

%S 2,1,1,2,4,7,14,29,61,129,282,623,1400,3189,7347,17101,40167,95110,

%T 226841,544555,1314983,3192458,7788521,19086807,46968280,116019696,

%U 287602234,715281652,1784383956,4464139806

%N Floor of the expected value of number of trials until exactly one cell is empty in a random distribution of n balls in n cells.

%C Also floor of the expected value of number of trials until we have n-1 distinct symbols in a random sequence on n symbols of length n. A055775 corresponds to zero cells empty.

%D W. Feller, An Introduction to Probability Theory and its Applications, 2nd ed, Wiley, New York, 1965, (2.4) p. 92. (Occupancy problems)

%H Washington Bomfim, <a href="/A210112/b210112.txt">Table of n, a(n) for n = 2..100</a>

%F With m = 1, a(n) = floor(n^n/(binomial(n,m)_Sum{v=0..n-m-1}((-1)^v*binomial(n-m,v) (n-m-v)^n)))

%e For n=2, with symbols 0 and 1, the 2^2 sequences on 2 symbols of length 2 can be represented by 00, 01, 10, and 11. We have 2 sequences with a unique symbol, so a(2) = floor(4/2) = 2.

%Y Cf. A055775, A209899, A209900, A210113, A210114, A210115, A210116.

%K nonn

%O 2,1

%A _Washington Bomfim_, Mar 18 2012

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Last modified September 28 01:20 EDT 2020. Contains 337388 sequences. (Running on oeis4.)