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#44 by Jean-François Alcover at Sun Sep 13 13:06:51 EDT 2015
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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.
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| STATUS
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approved
editing
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Discussion
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Sun Sep 13
| 13:07
| Jean-François Alcover: Added link to Chappell's paper
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#43 by N. J. A. Sloane at Sat Dec 06 18:02:11 EST 2014
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#42 by Jon E. Schoenfield at Sat Dec 06 16:20:58 EST 2014
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#41 by Jon E. Schoenfield at Sat Dec 06 16:20:55 EST 2014
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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:
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| EXAMPLE
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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}.
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approved
editing
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#40 by N. J. A. Sloane at Sat Nov 22 00:09:23 EST 2014
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#39 by Tilman Piesk at Sat Nov 15 04:36:32 EST 2014
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Discussion
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Sat Nov 15
| 04:42
| 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.
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| 05:47
| Michel Marcus: You can also try to email the user through his user's page.
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| Michel Marcus: Without 's see http://dx.doi.org/10.1016/j.disc.2004.07.020
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| 06:19
| 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.
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| 08:26
| Michel Marcus: I don't think so, but I can be wrong
Mostly wanted to give you link I found.
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#38 by Tilman Piesk at Fri Nov 07 20:54:01 EST 2014
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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.
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Discussion
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Sat Nov 15
| 01:54
| 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
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| 04:36
| 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.
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#37 by Tilman Piesk at Fri Nov 07 20:32:05 EST 2014
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Number of permutations of a multiset that contains m different elements n times. (compare array A249543, showing the signatures of these multisets).
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#36 by Tilman Piesk at Sat Nov 01 13:17:48 EDT 2014
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Number of permutations of a multiset that contains m times thedifferent elements of a n-set times.
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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>
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| EXAMPLE
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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}.
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#35 by Joerg Arndt at Thu Oct 30 14:38:56 EDT 2014
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Comment fromFrom Tilman Piesk, Oct 28 2014: (Start)
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Discussion
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Thu Oct 30
| 14:41
| Joerg Arndt: After checking the 6 seqs. containing 'A187783': the proposed change does not seem to break anything.
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