%I A152170
%S A152170 0,1,6,57,700,10505,186186,3805249,88099320,2278824849,65132155990,
%T A152170 2038428376721,69332064858420,2546464715771353,100444826158022178,
%U A152170 4234886922345707265,190053371487946575856,9045570064018726951457
%N A152170 a(n) is the total size of all the image sets of all functions from [n] 
               to [n]. I.e. a(n) is the sum of the cardinalities of every image 
               set of every function whose domain and co-domain is {1,2,...,n}.
%C A152170 a(n)/n^n is the expected value for the cardinality of the image set of 
               a function that takes [n] to [n]. a(n)/(n^(n+1)) is the probability 
               that any particular element of [n] will be in the range of a function 
               f:[n]to[n].
%F A152170 a(n)=n(n^n-(n-1)^n); a(n) = Sum_{i=1 to i=n} {n,i}i!(n,i)i where {n,i} 
               is the Stirling number of the second kind and (n,i) is the binomial 
               coefficient.
%e A152170 a(2)=6 because the image sets of the functions from [2] to [2] are {1},
               {2},{1,2},{1,2}
%t A152170 Table[Sum[StirlingS2[n, i] i! Binomial[n, i] i, {i, 1, n}], {n, 0, 20}] 
               [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 17 2009]
%Y A152170 Sequence in context: A060435 A153851 A141372 this_sequence A087659 A107718 
               A000406
%Y A152170 Adjacent sequences: A152167 A152168 A152169 this_sequence A152171 A152172 
               A152173
%K A152170 nonn
%O A152170 0,3
%A A152170 Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Nov 27 2008
%E A152170 Added more terms Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), Mar 
               17 2009