OFFSET
1,3
LINKS
Spencer Daugherty, Pamela E. Harris, Ian Klein, and Matt McClinton, Metered Parking Functions, arXiv:2406.12941 [math.CO], 2024.
FORMULA
T(n+k,n) = Sum_{sigma = (sigma_1, ..., sigma_n) in S_n} (( Product_{i=1..n} L_{i}(sigma))( Product_{j=1..k} sigma_j mod n )), where k>0 and L_{i}(sigma) is the largest index h with i<h for which sigma_i >= sigma_N for all N in {i-j, i-j+1, ..., i-1, i}.
EXAMPLE
Table begins:
1, 2, 3, 4, 5, 6, 7, ...
1, 3, 8, 15, 24, 35, 48, ...
1, 4, 16, 50, 108, 196, 320, ...
1, 6, 27, 125, 432, 1029, 2048, ...
1, 8, 48, 257, 1296, 4802, 12288, ...
1, 12, 96, 540, 3156, 16807, 65536, ...
1, 16, 162, 1200, 7734, 47442, 262144, ...
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Spencer Daugherty, Jul 18 2024
STATUS
approved