OFFSET
0,5
COMMENTS
The weak excedance set of a permutation p of [n] is the set of indices i such that p(i) >= i.
LINKS
Alois P. Heinz, Rows n = 0..20, flattened
Wikipedia, Permutation
FORMULA
T(n,floor(n^2/4)) = 1.
Sum_{k=0..floor(n^2/4)} k * T(n,k) = A395245(n).
EXAMPLE
T(n,0) = 4: 2143, 3142, 4123, 4132.
T(n,1) = 8: 1423, 2413, 3124, 3412, 3421, 4213, 4312, 4321.
T(n,2) = 11: 1243, 1324, 1342, 1432, 2134, 2314, 2341, 2431, 3214, 3241, 4231.
T(n,4) = 1: 1234.
Triangle T(n,k) begins:
1;
1;
1, 1;
2, 3, 1;
4, 8, 11, 0, 1;
12, 18, 63, 8, 18, 0, 1;
36, 39, 285, 104, 198, 0, 57, 0, 0, 1;
144, 81, 1104, 950, 1536, 0, 1104, 0, 39, 81, 0, 0, 1;
...
MAPLE
b:= proc(s, i, k) option remember; (n-> `if`(n=0, x^(i*k), add(
b(s minus {j}, `if`(irem(n, 2)=1 or j<n, 0, 1)+i,
`if`(irem(n, 2)=0 or j<n, 0, 1)+k), j=s)))(nops(s))
end:
T:= (n, k)-> coeff(b({$1..n}, 0$2), x, k):
seq(seq(T(n, k), k=0..(n^2)/4), n=0..10);
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Jul 15 2026
STATUS
approved