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A190295 A055134(n,k)*k 1
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 (list; table; graph; refs; listen; history; text; internal format)
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: A279504 A279994 A307659 * A228154 A275279 A109767

Adjacent sequences:  A190292 A190293 A190294 * A190296 A190297 A190298

KEYWORD

nonn,tabl

AUTHOR

Geoffrey Critzer, May 07 2011

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)