OFFSET
1,2
COMMENTS
Also the number of k-dimensional flats of the extended Shi arrangement of dimension n consisting of hyperplanes x_i - x_j = d (1 <= i < j <= n, -2 <= d <= 3).
LINKS
N. Nakashima and S. Tsujie, Enumeration of Flats of the Extended Catalan and Shi Arrangements with Species, arXiv:1904.09748 [math.CO], 2019.
FORMULA
E.g.f.: exp(x*y/(1-3*x)).
T(n,k) = 3^(n-k)*binomial(n-1, k-1)*n!/k! = 3^(n-k)*A105278.
EXAMPLE
Triangle begins:
1;
6, 1;
54, 18, 1;
648, 324, 36, 1;
9720, 6480, 1080, 60, 1;
...
MATHEMATICA
Table[3^(n - k) * Binomial[n - 1, k - 1] * n! / k!, {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 13 2019 *)
CROSSREFS
KEYWORD
AUTHOR
Shuhei Tsujie, May 18 2019
STATUS
approved