OFFSET
0,3
COMMENTS
Number of upper triangular n X n {0,1,...,n}-matrices with no zero rows or columns.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..35
Hsien-Kuei Hwang, Emma Yu Jin, and Michael J. Schlosser, Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow, arXiv:2012.13570 [math.CO], 2020.
Vít Jelínek, Counting general and self-dual interval orders, Journal of Combinatorial Theory, Series A, Volume 119, Issue 3, April 2012, pp. 599-614; arXiv preprint, arXiv:1106.2261 [math.CO], 2011.
Wikipedia, Peter C. Fishburn
FORMULA
a(n) = [x^n] Sum_{j=0..n} x^j * Product_{i=1..j} ((n+1)^i-1)/(1+x*((n+1)^i-1)).
EXAMPLE
a(0) = 1: [].
a(1) = 1: [1].
a(2) = 12:
[10] [10] [20] [20] [11] [11] [21] [21] [12] [12] [22] [22]
[ 1] [ 2] [ 1] [ 2] [ 1] [ 2] [ 1] [ 2] [ 1] [ 2] [ 1] [ 2].
MAPLE
a:= n-> coeff(series(add(x^j*mul(((n+1)^i-1)/(1+x*
((n+1)^i-1)), i=1..j), j=0..n), x, n+1), x, n):
seq(a(n), n=0..10);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 20 2024
STATUS
approved