OFFSET
1,2
COMMENTS
Also the number of k-dimensional flats of the extended Catalan arrangement of dimension n consisting of hyperplanes x_i - x_j = d (1 <= i < j <= n, -2 <= d <= 2).
LINKS
Robert Gill, The number of elements in a generalized partition semilattice, Discrete mathematics 186.1-3 (1998): 125-134.
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((exp(x)-1)*y/(3-2exp(x))).
EXAMPLE
Triangle begins:
1;
5, 1;
37, 15, 1;
365, 223, 30, 1;
4501, 3675, 745, 50, 1;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Shuhei Tsujie, May 27 2019
STATUS
approved