OFFSET
0,4
COMMENTS
Row sums are A006472(n+1).
T(n, binomial(n,2)-k) is the number of rank-k intervals in the middle order on permutations. (See Bouvel et al. reference.) - Bridget Tenner, May 24 2024
LINKS
Alois P. Heinz, Rows n = 0..50, flattened
Mathilde Bouvel, Luca Ferrari, and Bridget Eileen Tenner, Between weak and Bruhat: the middle order on permutations, arXiv:2405.08943 [math.CO], 2024.
FORMULA
From Alois P. Heinz, May 24 2024: (Start)
|Sum_{k=0..binomial(n,2)} (-1)^k T(n,k)| = A010551(n).
Sum_{k=0..binomial(n,2)} (binomial(n,2)-k)*T(n,k) = A259459(n-2) for n>=2. (End)
EXAMPLE
Triangle T(n,k) begins:
1;
1;
1, 2;
1, 4, 7, 6;
1, 6, 18, 36, 49, 46, 24;
1, 8, 33, 94, 204, 354, 497, 562, 501, 326, 120;
...
MATHEMATICA
a := Table[CoefficientList[Product[Sum[D[x^i, x], {i, 1, m}], {m, 1, n}], x], {n, 0, 7}]; Flatten[a]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Roger L. Bagula, Jun 13 2008
EXTENSIONS
Edited by Alois P. Heinz, May 24 2024
STATUS
approved