OFFSET
0,6
COMMENTS
Equivalently, this is the number of preference lists of n cars on k spots so that only n - k cars are unable to park.
LINKS
P. J. Cameron, D. Johannsen, T. Prellberg, and P. Schweitzer, Counting Defective Parking Functions, Electronic Journal of Combinatorics, Volume 15 (2008).
FORMULA
T(n, k) = k^n - Sum_{i=0..k-1} binomial(n, i)*(i+1)^(i-1)*(k-i-1)^(n-i).
T(n, k) = Sum_{i=k..n} (-1)^(n-i)*binomial(n, i)*(i+1)^(i-1)*(i-k+1)^(n-i).
EXAMPLE
Table begins:
1;
0, 1;
0, 1, 3;
0, 1, 7, 16;
0, 1, 15, 61, 125;
0, 1, 31, 206, 671, 1296;
0, 1, 63, 659, 3130, 9031, 16807;
0, 1, 127, 2052, 13686, 54062, 144495, 262144;
0, 1, 255, 6297, 57867, 301321, 1059261, 2685817, 4782969;
0, 1, 511, 19162, 240049, 1616764, 7196785, 23343742, 56953279, 100000000;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jayden Thadani and Alan Kappler, May 23 2024
STATUS
approved