A199656 Triangular array read by rows, T(n,k) is the number of functions from {1,2,...,n} into {1,2,...,n} with maximum value of k.

1, 1, 3, 1, 7, 19, 1, 15, 65, 175, 1, 31, 211, 781, 2101, 1, 63, 665, 3367, 11529, 31031, 1, 127, 2059, 14197, 61741, 201811, 543607, 1, 255, 6305, 58975, 325089, 1288991, 4085185, 11012415, 1, 511, 19171, 242461, 1690981, 8124571, 30275911, 93864121, 253202761

Offset: 1

Author

Geoffrey Critzer, Nov 08 2011

Keywords

• nonn
• easy
• tabl

Comments

Row sums = A000312.

Main diagonal = A045531.

Examples

			Triangle begins:
  1
  1    3
  1    7   19
  1   15   65   175
  1   31  211   781   2101
  1   63  665  3367  11529   31031
  1  127 2059 14197  61741  201811  543607
  ...
		

Links

• Vincenzo Librandi, Rows n = 1..60, flattened

Crossrefs

Cf. A022522, A022523.

Programs

Magma

/* As triangle: */ [[k^n - (k-1)^n: k in [1..n]]: n in [1..9]]; // Vincenzo Librandi, Jan 28 2013

Mathematica

Table[Table[(1-((i-1)/i)^n) i^n,{i,1,n}],{n,1,8}]//Grid
Flatten[Table[k^n - (k-1)^n, {n, 0, 10}, {k, 1, n}]] (* Vincenzo Librandi, Jan 28 2013 *)

Formula

T(n,k) = k^n-(k-1)^n.