OFFSET
1,2
COMMENTS
Start with the n! permutations of order n. Apply an iteration of the "optimist" sorting algorithm. Count the distinct permutations, until all are sorted.
The length of each row is n.
The optimist algorithm is: rotate right all currently unsorted letters by the distance between the first unsorted one and its sorted position. An example is given in A345453.
FORMULA
T(n,0) = n!; T(n,n-1) = 1; T(n,n-2) = 1 for n > 2.
EXAMPLE
Triangle begins:
.
1;
2, 1;
6, 1, 1;
24, 6, 1, 1;
120, 38, 7, 1, 1;
720, 232, 53, 7, 1, 1;
5040, 1607, 404, 74, 7, 1, 1;
.
CROSSREFS
KEYWORD
tabl,nonn
AUTHOR
Olivier Gérard, Jun 20 2021
STATUS
approved