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.

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

Offset: 6

Author

Washington Bomfim, Mar 18 2012

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A055775, A209899, A209900, A210112, A210113, A210114, A210115.

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)))