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A369336 Number of n X n Fishburn matrices with entries in the set {0,1,...,n}.

%I A369336 #16 Jan 22 2024 17:52:01
%S A369336 1,1,12,2052,5684480,305416893750,391129148721673152,
%T A369336 14286237711414132094989064,17309880507327972883933887341789184,
%U A369336 792117985317303404452447777723478865406570410,1534214120588806182890487155420702132205591283310000000000
%N A369336 Number of n X n Fishburn matrices with entries in the set {0,1,...,n}.
%C A369336 Number of upper triangular n X n {0,1,...,n}-matrices with no zero rows or columns.
%H A369336 Alois P. Heinz, <a href="/A369336/b369336.txt">Table of n, a(n) for n = 0..35</a>
%H A369336 Hsien-Kuei Hwang, Emma Yu Jin, and Michael J. Schlosser, <a href="https://arxiv.org/abs/2012.13570">Asymptotics and statistics on Fishburn Matrices: dimension distribution and a conjecture of Stoimenow</a>, arXiv:2012.13570 [math.CO], 2020.
%H A369336 Vít Jelínek, <a href="http://dx.doi.org/10.1016/j.jcta.2011.11.010">Counting general and self-dual interval orders</a>, Journal of Combinatorial Theory, Series A, Volume 119, Issue 3, April 2012, pp. 599-614; <a href="http://arxiv.org/abs/1106.2261">arXiv preprint</a>, arXiv:1106.2261 [math.CO], 2011.
%H A369336 Wikipedia, <a href="https://en.wikipedia.org/wiki/Peter_C._Fishburn">Peter C. Fishburn</a>
%F A369336 a(n) = [x^n] Sum_{j=0..n} x^j * Product_{i=1..j} ((n+1)^i-1)/(1+x*((n+1)^i-1)).
%e A369336 a(0) = 1: [].
%e A369336 a(1) = 1: [1].
%e A369336 a(2) = 12:
%e A369336   [10] [10] [20] [20]  [11] [11] [21] [21]  [12] [12] [22] [22]
%e A369336   [ 1] [ 2] [ 1] [ 2]  [ 1] [ 2] [ 1] [ 2]  [ 1] [ 2] [ 1] [ 2].
%p A369336 a:= n-> coeff(series(add(x^j*mul(((n+1)^i-1)/(1+x*
%p A369336     ((n+1)^i-1)), i=1..j), j=0..n), x, n+1), x, n):
%p A369336 seq(a(n), n=0..10);
%Y A369336 Cf. A000007, A005321, A289314, A289315.
%Y A369336 Main diagonal of A369415.
%K A369336 nonn
%O A369336 0,3
%A A369336 _Alois P. Heinz_, Jan 20 2024