A140907 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.
1, 120, 4950, 108900, 1557270, 16195608, 131589315, 877262100, 4971151900, 24584605760, 108284013552, 431621592480, 1577078895600, 5337805492800, 16880809870980, 50245234086564, 141622596077325, 379998709805000, 974996689631250, 2401570793407500
Offset: 0
Keywords
Links
- Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 25.
Formula
(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))