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

0,6

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.

Links

Table of n, a(n) for n=0..35.

Example

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...

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

Crossrefs

Sequence in context: A268308 A027606 A202693 * A083679 A213930 A319463

Adjacent sequences: A174549 A174550 A174551 * A174553 A174554 A174555

Keyword

nonn,tabl

Author

Geoffrey Critzer, Mar 22 2010

Status

approved