cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A210112 #9 Mar 30 2012 18:52:23
%S A210112 2,1,1,2,4,7,14,29,61,129,282,623,1400,3189,7347,17101,40167,95110,
%T A210112 226841,544555,1314983,3192458,7788521,19086807,46968280,116019696,
%U A210112 287602234,715281652,1784383956,4464139806
%N 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.
%C A210112 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.
%D A210112 W. Feller, An Introduction to Probability Theory and its Applications, 2nd ed, Wiley, New York, 1965, (2.4) p. 92. (Occupancy problems)
%H A210112 Washington Bomfim, <a href="/A210112/b210112.txt">Table of n, a(n) for n = 2..100</a>
%F A210112 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)))
%e A210112 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.
%Y A210112 Cf. A055775, A209899, A209900, A210113, A210114, A210115, A210116.
%K A210112 nonn
%O A210112 2,1
%A A210112 _Washington Bomfim_, Mar 18 2012