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%I #7 Mar 31 2012 20:17:50
%S 625,50,13,5,3,2,2,2,3,4,5,7,11,17,28,46,78,136,242,441,815,1533,2927,
%T 5669,11123,22090,44363,90027,184482,381499,795686,1672914,3543925,
%U 7561129,16240832,35106812,76346759,166982782,367206632,811693449
%N Floor of the expected value of number of trials until exactly four cells are 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-4 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 W. Bomfim, <a href="/A210115/b210115.txt">Table of n, a(n) for n = 5..100</a>
%F With m = 4, 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=5, there are 5^5 = 3125 sequences on 5 symbols of length 5. Only 5 sequences has a unique symbol, so a(5) = floor(3125/5) = 625.
%Y Cf. A055775, A209899, A209900, A210112, A210113, A210114, A210116.
%K nonn
%O 5,1
%A _Washington Bomfim_, Mar 18 2012
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