A190295 A055134(n,k)*k.

1, 2, 2, 12, 12, 3, 108, 108, 36, 4, 1280, 1280, 480, 80, 5, 18750, 18750, 7500, 1500, 150, 6, 326592, 326592, 136080, 30240, 3780, 252, 7, 6588344, 6588344, 2823576, 672280, 96040, 8232, 392, 8

Offset: 1

Author

Geoffrey Critzer, May 07 2011

Keywords

• nonn
• tabl

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

Examples

			Triangle begins
1
2     2
12    12    3
108   108   36    4
1280  1280  480   80    5
18750 18750 7500  1500  150   6
		

Programs

Mathematica

Flatten[CoefficientList[Table[Series[n((n-1)+x)^(n-1),{x,0,20}],{n,1,8}],x]]

Formula

O.g.f. for row n: n*((n-1)+x)^(n-1)