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.
%I A209081 #7 Mar 30 2012 18:52:23
%S A209081 1,1,2,2,3,3,4,5,5,6,7,7,8,9,9,10,10,11,12,12,13,14,14,15,15,16,17,17,
%T A209081 18,19,19,20,21,21,22,22,23,24,24,25,26,26,27,27,28,29,29,30,31,31,32,
%U A209081 33,33,34,34,35,36,36,37,38
%N A209081 Floor(A152170(n)/n^n). Floor of the expected value of the cardinality of the image of a function from [n] to [n].
%C A209081 From the first commentary of A152170, a(n)= floor(A152170(n)/n^n) = floor((n(n^n-(n-1)^n))/n^n) = floor(n-(n-1)^n/n^(n-1)).
%H A209081 Washington Bomfim, <a href="/A208846/a208846.txt">A method to find bijections from a set of n integers to {0,1, ... ,n-1}</a>
%F A209081 a(n) = floor(n-(n-1)^n/n^(n-1)).
%e A209081 a(1) = 1 because the image of a function from [1] to [1] has one value. a(2) = 1 since we can consider functions with domain {x,y}, and image {X,Y}. We can have f(x)=X, f(y)=X; f(x)=X, f(y)=Y; f(x)=Y, f(y)=Y; f(x)=Y, f(y)=X.
%e A209081 The sum of the cardinalities of the images divided by the number of functions is (1+2+1+2)/4 = 1.5. Floor(1.5)=1.
%Y A209081 Cf. A152170.
%K A209081 nonn
%O A209081 1,3
%A A209081 _Washington Bomfim_, Mar 05 2012