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

1,2

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

Links

Table of n, a(n) for n=1..36.

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

Sequence in context: A350784 A307659 A327874 * A228154 A275279 A109767

Adjacent sequences: A190292 A190293 A190294 * A190296 A190297 A190298

Keyword

nonn,tabl

Author

Geoffrey Critzer, May 07 2011

Status

approved