Search: id:A048601
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%I A048601
%S A048601 1,1,1,2,3,2,7,14,14,7,42,105,135,105,42,429,1287,2002,2002,1287,429,
%T A048601 7436,26026,47320,56784,47320,26026,7436,218348,873392,1813968,2519400,
%U A048601 2519400,1813968,873392,218348,10850216,48825972,113927268,179028564
%N A048601 Robbins triangle read by rows: T(n,k) = number of alternating sign n 
               X n matrices with a 1 at top of column k (n >= 1, 1<=k<=n)
%C A048601 An alternating sign matrix is a matrix of 0's and 1's such that (a) the 
               sum of each row and column is 1; (b) the nonzero entries in each 
               row and column alternate in sign.
%D A048601 D. Bressoud, Proofs and Confirmations: The Story of the Alternating Sign 
               Matrix Conjecture, Cambridge University Press, 1999, p. 5.
%D A048601 D. Bressoud and J. Propp, How the alternating sign matrix conjecture 
               was solved, Notices Amer. Math. Soc., 46 (No. 6, 1999), 637-646.
%D A048601 D. Zeilberger, Dave Robbins's Art of Guessing, Adv. in Appl. Math. 34 
               (2005), 939-954.
%H A048601 N. J. A. Sloane, <a href="b048601.txt">Table of n, a(n) for n = 1..1275</
               a> [Rows 1..50, flattened]
%H A048601 P. Di Francesco, <a href="http://arXiv.org/abs/cond-mat/0409576">A refined 
               Razumov-Stroganov conjecture II</a>
%H A048601 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AlternatingSignMatrix.html">Link to a section of The World of Mathematics.</
               a>
%H A048601 D. Zeilberger, <a href="http://arXiv.org/abs/math.CO/9606224">[math/9606224] 
               Proof of the Refined Alternating Sign Matrix Conjecture</a>
%F A048601 T(n, k)=binomial(n+k-2, k-1)*((2*n-k-1)!/(n-k)!)*product(((3*j+1)!/(n+j)!), 
               j=0..n-2);
%e A048601 Triangle begins:
%e A048601 1,
%e A048601 1,1,
%e A048601 2,3,2,
%e A048601 7,14,14,7,
%e A048601 42,105,135,105,42,
%e A048601 429,1287,2002,2002,1287,429,
%e A048601 7436,26026,47320,56784,47320,26026,7436,
%e A048601 ...
%p A048601 T:=(n,k)-> binomial(n+k-2, k-1)*((2*n-k-1)!/(n-k)!)*product(((3*j+1)!/
               (n+j)!),j=0..n-2);
%Y A048601 Row sums (also borders) of triangle give A005130. Cf. A051106.
%Y A048601 Sequence in context: A129022 A122076 A014784 this_sequence A008317 A139011 
               A152297
%Y A048601 Adjacent sequences: A048598 A048599 A048600 this_sequence A048602 A048603 
               A048604
%K A048601 nonn,tabl,nice,easy
%O A048601 1,4
%A A048601 N. J. A. Sloane (njas(AT)research.att.com).
%E A048601 More terms from James A. Sellers (sellersj(AT)math.psu.edu)

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