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A263216 Triangle read by rows: T(n>=2, k>=1) is the number of Dyck paths of length 2n that correspond to k alternating sign matrices. 0

%I #14 Oct 19 2015 12:17:30

%S 2,3,2,5,4,0,0,3,0,2,8,10,0,0,6,0,4,0,0,0,0,0,0,5,0,0,0,0,0,0,4,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,2,13,20,0,4,15,0,10,0,0,0,0,0,0,10,

%U 0,0,0,0,0,0,8,0,0,0,0,0,0,0,0,0,0,0,0,0,6,0,0,0,0,0,0,12,0,0,0,0,0,0

%N Triangle read by rows: T(n>=2, k>=1) is the number of Dyck paths of length 2n that correspond to k alternating sign matrices.

%C Row sums give A000108, n >= 2.

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000079">The number of alternating sign matrices for a given Dyck path</a>.

%e Triangle begins:

%e 2,

%e 3,2,

%e 5,4,0,0,3,0,2,

%e 8,10,0,0,6,0,4,0,0,0,0,0,0,5,0,0,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,2,

%e ...

%Y Cf. A000108.

%K nonn,tabf

%O 2,1

%A _Christian Stump_, Oct 19 2015

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