A174552 Triangular array T(n,k): The differences in the columns of A174551.

1, 0, 1, 1, 1, 2, 8, 7, 6, 6, 81, 65, 50, 36, 24, 1024, 781, 570, 390, 240, 120, 15625, 11529, 8162, 5460, 3360, 1800, 720, 279936, 201811, 140070, 92526, 57120, 31920, 15120, 5040

Offset: 0

Author

Geoffrey Critzer, Mar 22 2010

Keywords

• nonn
• tabl

Comments

T(n,k) is the number of functions f:{1,2,...,n}->{1,2,...,n} such that the image of f contains {1,2,...,k} but not k+1.

Row sums = n^n.

Columns are asymptotic to n^n (1/e)(1-(1/e))^k.

Sum k*T(n,k) appears to be A055869.

Examples

			Triangle begins:
1;
0, 1;
1, 1, 2;
8, 7, 6, 6;
81,65,50,36,24;
1024,781,570,390,240,120;
15625, 11529, 8162, 5460, 3360, 1800, 720...
		

Programs

Mathematica

Table[Append[(-1) Differences[ Table[Sum[(-1)^i Binomial[k, i] (n - i)^n, {i, 0, k}], {k, 0, n}]], n! ], {n, 0, 7}] // Grid