OFFSET
1,2
COMMENTS
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.
Row sums = A000312 = n^n so we see the expected number of fixed points is 1.
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
FORMULA
O.g.f. for row n: n*((n-1)+x)^(n-1)
EXAMPLE
Triangle begins
1
2 2
12 12 3
108 108 36 4
1280 1280 480 80 5
18750 18750 7500 1500 150 6
MATHEMATICA
Flatten[CoefficientList[Table[Series[n((n-1)+x)^(n-1), {x, 0, 20}], {n, 1, 8}], x]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, May 07 2011
STATUS
approved