

A209081


Floor(A152170(n)/n^n). Floor of the expected value of the cardinality of the image of a function from [n] to [n].


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OFFSET

1,3


COMMENTS

From the first commentary of A152170, a(n)= floor(A152170(n)/n^n) = floor((n(n^n(n1)^n))/n^n) = floor(n(n1)^n/n^(n1)).


LINKS



FORMULA

a(n) = floor(n(n1)^n/n^(n1)).


EXAMPLE

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.
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.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



