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Triangle read by rows: T(n,k) is the number of white corners of rank k in all the permutations of {1,2,...,n} (n>=2, 0<=k<=n-2; for definitions see the Eriksson-Linusson references).
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%I #6 Nov 28 2018 12:19:35

%S 1,5,1,26,9,2,154,70,26,6,1044,562,268,102,24,8028,4860,2700,1308,504,

%T 120,69264,45756,28224,15828,7728,3000,720

%N Triangle read by rows: T(n,k) is the number of white corners of rank k in all the permutations of {1,2,...,n} (n>=2, 0<=k<=n-2; for definitions see the Eriksson-Linusson references).

%C Sum of row n is A140712(n).

%C T(n,0) = A001705(n-1).

%C T(n,n-2) = (n-2)!.

%D K. Eriksson and S. Linusson. Combinatorics of Fulton's essential set. Duke Mathematical Journal 85(1):61-76, 1996.

%H K. Eriksson and S. Linusson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v2i1r6">The size of Fulton's essential set</a>, Electronic J. Combinatorics, Vol. 2, #R6, 1995.

%H K. Eriksson and S. Linusson, <a href="https://www.researchgate.net/publication/2550835_Combinatorics_of_Fulton&#39;s_essential_set">Combinatorics of Fulton's essential set</a>, ResearchGate, 1998.

%e Triangle starts:

%e 1;

%e 5,1;

%e 26,9,2;

%e 154,70,26,6;

%e 1044,562,268,102,24;

%Y Cf. A001705, A140711, A140712.

%K nonn,tabl,more

%O 2,2

%A _Emeric Deutsch_, May 29 2008