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 A210116 Floor of the expected value of number of trials until exactly five cells are empty in a random distribution of n balls in n cells. 5
 7776, 311, 51, 16, 7, 4, 3, 3, 2, 3, 3, 4, 5, 8, 11, 16, 25, 40, 66, 110, 187, 325, 574, 1032, 1885, 3492, 6557, 12467, 23988, 46667, 91731, 182078, 364734, 736972, 1501318, 3082136, 6374007, 13273719, 27825438, 58697777, 124566798 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,1 COMMENTS Also floor of the expected value of number of trials until we have n-5 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 W. Bomfim, Table of n, a(n) for n = 6..100 FORMULA With m = 5, 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=6, there are 6^6 = 46656 sequences on 6 symbols of length 6. Only 6 sequences has a unique symbol, so a(6) = floor(46656/6) = 7776. CROSSREFS Cf. A055775, A209899, A209900, A210112, A210113, A210114, A210115. Sequence in context: A028538 A123990 A176375 * A223509 A187355 A190465 Adjacent sequences:  A210113 A210114 A210115 * A210117 A210118 A210119 KEYWORD nonn AUTHOR Washington Bomfim, Mar 18 2012 STATUS approved

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Last modified September 24 04:42 EDT 2020. Contains 337317 sequences. (Running on oeis4.)