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

6,1

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: A354976 A123990 A176375 * A223509 A187355 A190465

Adjacent sequences: A210113 A210114 A210115 * A210117 A210118 A210119

Keyword

nonn

Author

Washington Bomfim, Mar 18 2012

Status

approved