

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
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OFFSET

3,1


COMMENTS

Also floor of the expected value of number of trials until we have n2 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 = 3..100


FORMULA

With m = 2, a(n) = floor(n^n/(binomial(n,m)*_Sum{v=0..nm1}((1)^v*binomial(nm,v)*(nmv)^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.


CROSSREFS

Cf. A055775, A209899, A209900, A210112, A210114, A210115, A210116.
Sequence in context: A306808 A086232 A133867 * A195704 A176516 A210644
Adjacent sequences: A210110 A210111 A210112 * A210114 A210115 A210116


KEYWORD

nonn


AUTHOR

Washington Bomfim, Mar 18 2012


STATUS

approved



