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%I #16 Jun 26 2013 10:57:23
%S 1,2,2,12,12,3,108,108,36,4,1280,1280,480,80,5,18750,18750,7500,1500,
%T 150,6,326592,326592,136080,30240,3780,252,7,6588344,6588344,2823576,
%U 672280,96040,8232,392,8
%N A055134(n,k)*k
%C Triangular array read by rows. T(n,k) is the total number of fixed points in the endofunctions on {1,2,...,n} that have exactly k fixed points.
%C Row sums = A000312 = n^n so we see the expected number of fixed points is 1.
%C T(n,k) is also the number of endofunctions f:{1,2,...,n}->{1,2,...,n} in which there are exactly k elements j in {1,2,...,n-1} such that f(j)= f(j+1). - _Geoffrey Critzer_, Jun 25 2013
%F O.g.f. for row n: n*((n-1)+x)^(n-1)
%e Triangle begins
%e 1
%e 2 2
%e 12 12 3
%e 108 108 36 4
%e 1280 1280 480 80 5
%e 18750 18750 7500 1500 150 6
%t Flatten[CoefficientList[Table[Series[n((n-1)+x)^(n-1),{x,0,20}],{n,1,8}],x]]
%K nonn,tabl
%O 1,2
%A _Geoffrey Critzer_, May 07 2011
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