A373086 Triangle read by rows: T(n, k) is the number of parking functions of length n with preferences restricted to {1, ..., k} for 0 <= k <= n.
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
Offset: 0
Examples
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; ...
Links
- P. J. Cameron, D. Johannsen, T. Prellberg, and P. Schweitzer, Counting Defective Parking Functions, Electronic Journal of Combinatorics, Volume 15 (2008).
Crossrefs
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).
Comments