A209899 Floor of the expected number of empty cells in a random placement of 2n balls into n cells.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11

Offset: 1

Author

Washington Bomfim, Mar 14 2012

Keywords

• nonn

References

• W. Feller, An Introduction to Probability Theory and its Applications, 2nd ed, Wiley, New York, 1965, p. 226.

Crossrefs

Cf. A209900.

Programs

Mathematica

Table[Floor[n*(1 - 1/n)^(2 n)], {n, 100}] (* T. D. Noe, Mar 15 2012 *)

Formula

a(n) = floor(n*(1-1/n)^(2n)).