T. Chappell, A. Lascoux, S. Ole Warnaar, W. Zudilin, <a href="http://arxiv.org/abs/1112.3130">Logarithmic and complex constant term identities</a>, arXiv:1112.3130 [math.CO], 2012.

approved

editing

Jean-François Alcover: Added link to Chappell's paper

proposed

approved

editing

proposed

In an m-dimensional Pascal tensor (the generalisationgeneralization of a symmetric Pascal matrix) P(x1,...,xn) = (x1+...+xn)!/(x1!*...*xn!), so the main diagonal of an m-dimensional Pascal tensor is D(n) = (m*n)!/(n!^m). These diagonals are the rows of this array (with m>0), which begins like this:

T(3,5) = (3*5)!/(5!^3) = 756756 = A014609(3) = A006480(5) is the number of permutations of a multiset that contains 3 different elements 5 times, e.g. {., {1,1,1,1,1,2,2,2,2,2,3,3,3,3,3}.

approved

editing

proposed

approved

editing

proposed

Tilman Piesk: BTW, if you Google "De Bruijn's triangle" you will find only this article, and a De Bruijn's sequence seems to be something completely different.

Michel Marcus: You can also try to email the user through his user's page.

Michel Marcus: Without 's see http://dx.doi.org/10.1016/j.disc.2004.07.020

Tilman Piesk: And our triangle here is part of what the Shapiros and Vainshtein are doing there? If this is not "the" but "a De Bruijn triangle" we should include some parameters in the description.

Michel Marcus: I don't think so, but I can be wrong
Mostly wanted to give you link I found.

Number of permutations of a multiset that contains m different elements n times (compare. These arraymultisets A249543, showinghave the signatures A249543(m,n-1) for ofm>=1 theseand multisets).n>=2.

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A187783 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

Tilman Piesk: Robert did not respond. I think the inclusion of row 0 is no bigger deal than the inclusion of element 0 in A172603 etc. (all the columns have index 0 now). I propose the sequence again as it is now.

Number of permutations of a multiset that contains m different elements n times. (compare array A249543, showing the signatures of these multisets).

Number of permutations of a multiset that contains m times thedifferent elements of a n-set times.

Tilman Piesk, <a href="https://commons.wikimedia.org/wiki/File:Multisets_that_contain_m_different_elements_n_times.svg">Illustration of the multisets for m,n=0..4</a>

T(3,5) = (3*5)!/(5!^3) = 756756 = A014609(3) = A006480(5) is the number of permutations of a multiset that contains 3 times thedifferent elements of a 5-set times, e.g. {1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,5,53,53}.

Comment fromFrom Tilman Piesk, Oct 28 2014: (Start)

Joerg Arndt: After checking the 6 seqs. containing 'A187783': the proposed change does not seem to break anything.