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%I #7 Jan 17 2025 09:28:50
%S 1,120,4950,108900,1557270,16195608,131589315,877262100,4971151900,
%T 24584605760,108284013552,431621592480,1577078895600,5337805492800,
%U 16880809870980,50245234086564,141622596077325,379998709805000,974996689631250,2401570793407500
%N Number of 3 X 7 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,7,n can be permuted, see formula.
%H Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See p. 25.
%F (empirical) set p,q,r to n,7,3 (in any order) in s=p+q+r-1; a(n) = product {i in 0..r-1} (binomial(s,p+i)*i!/(s-i)^(r-i-1))
%K nonn
%O 0,2
%A _R. H. Hardin_, Jul 05 2008