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A210113
Floor of the expected value of number of trials until exactly two cells are empty in a random distribution of n balls in n cells.
5
9, 3, 2, 1, 2, 3, 4, 7, 12, 21, 40, 75, 147, 292, 594, 1229, 2582, 5499, 11859, 25868, 57008, 126814, 284523, 643401, 1465511, 3360493, 7753730, 17993787, 41982506, 98445184, 231932762, 548839352, 1304155087
OFFSET
3,1
COMMENTS
Also floor of the expected value of number of trials until we have n-2 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
FORMULA
With m = 2, 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=3, there are 3^3 = 27 sequences on 3 symbols of length 3. Only 3 sequences has a unique symbol, so a(3) = floor(27/3) = 9.
KEYWORD
nonn
AUTHOR
Washington Bomfim, Mar 18 2012
STATUS
approved