The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number
of 
"bordered" alternating
sign matrices 
with a 1 at the top of column 
are, respectively, the numbers in the (2, 1)- and (1, 2)-Pascal
triangles which are different from 1. This conjecture was proven by Zeilberger (1996).
Refined Alternating Sign Matrix Conjecture
See also
Alternating Sign Matrix, Alternating Sign Matrix ConjectureExplore with Wolfram|Alpha
References
Bressoud, D. and Propp, J. "How the Alternating Sign Matrix Conjecture was Solved." Not. Amer. Math. Soc. 46, 637-646.Zeilberger, D. "Proof of the Refined Alternating Sign Matrix Conjecture." New York J. Math. 2, 59-68, 1996.Referenced on Wolfram|Alpha
Refined Alternating Sign Matrix ConjectureCite this as:
Weisstein, Eric W. "Refined Alternating Sign Matrix Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RefinedAlternatingSignMatrixConjecture.html