OFFSET
0,3
LINKS
Alois P. Heinz, Rows n = 0..141, flattened
Peter J. Cameron, Daniel Johannsen, Thomas Prellberg, Pascal Schweitzer, Counting Defective Parking Functions, arXiv:0803.0302 [math.CO], 2008
FORMULA
EXAMPLE
T(2,0) = 3: [1,1], [1,2], [2,1].
T(2,1) = 1: [2,2].
T(3,1) = 10: [1,3,3], [2,2,2], [2,2,3], [2,3,2], [2,3,3], [3,1,3], [3,2,2], [3,2,3], [3,3,1], [3,3,2].
T(3,2) = 1: [3,3,3].
Triangle T(n,k) begins:
0 : 1;
1 : 1;
2 : 3, 1;
3 : 16, 10, 1;
4 : 125, 107, 23, 1;
5 : 1296, 1346, 436, 46, 1;
6 : 16807, 19917, 8402, 1442, 87, 1;
7 : 262144, 341986, 173860, 41070, 4320, 162, 1;
8 : 4782969, 6713975, 3924685, 1166083, 176843, 12357, 303, 1;
...
MAPLE
S:= (n, k)-> `if`(k=0, n^n, add(binomial(n, i)*k*
(k+i)^(i-1)*(n-k-i)^(n-i), i=0..n-k)):
T:= (n, k)-> S(n, k)-S(n, k+1):
seq(seq(T(n, k), k=0..max(0, n-1)), n=0..10);
MATHEMATICA
S[n_, k_] := If[k==0, n^n, Sum[Binomial[n, i]*k*(k+i)^(i-1)*(n-k-i)^(n-i), {i, 0, n-k}]]; T[n_, k_] := S[n, k]-S[n, k+1]; T[0, 0] = 1; Table[T[n, k], {n, 0, 10}, {k, 0, Max[0, n-1]}] // Flatten (* Jean-François Alcover, Feb 18 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Alois P. Heinz, Nov 28 2015
STATUS
approved