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.

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

Offset: 2

Author

Washington Bomfim, Mar 18 2012

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A055775, A209899, A209900, A210113, A210114, A210115, A210116.

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)))