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

Offset

1,3

Comments

Row sums = A000312.

Main diagonal = A045531.

Links

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

Formula

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

Example

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 etc.

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 *)

Prog

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

Crossrefs

Cf. A022522, A022523.

Sequence in context: A282605 A281525 A096643 * A221345 A036575 A347485

Adjacent sequences: A199653 A199654 A199655 * A199657 A199658 A199659

Keyword

nonn,easy,tabl

Author

Geoffrey Critzer, Nov 08 2011

Status

approved