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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
 2, 1, 1, 2, 4, 7, 14, 29, 61, 129, 282, 623, 1400, 3189, 7347, 17101, 40167, 95110, 226841, 544555, 1314983, 3192458, 7788521, 19086807, 46968280, 116019696, 287602234, 715281652, 1784383956, 4464139806 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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. REFERENCES W. Feller, An Introduction to Probability Theory and its Applications, 2nd ed, Wiley, New York, 1965, (2.4) p. 92. (Occupancy problems) LINKS Washington Bomfim, Table of n, a(n) for n = 2..100 FORMULA 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))) EXAMPLE 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. CROSSREFS Cf. A055775, A209899, A209900, A210113, A210114, A210115, A210116. Sequence in context: A333272 A119558 A333450 * A024735 A024957 A153914 Adjacent sequences:  A210109 A210110 A210111 * A210113 A210114 A210115 KEYWORD nonn AUTHOR Washington Bomfim, Mar 18 2012 STATUS approved

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)