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%I #15 Aug 29 2019 17:19:28
%S 1,0,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,
%T 1,1,0,0,0,0,1,2,1,1,1,0,0,0,1,0,1,2,1,1,1,0,0,0,0,1,0,1,2,1,1,1,0,0,
%U 0,0,0,2,1,2,2,1,1,1,0,0,0,0,0,1,2,1,2,2,1,1,1,0,0,0,0,0,0,1,2,1,2,2,1,1,1
%N Triangle for number of partitions which define multiset repetition classes.
%C For definitions, references, links and examples see the corresponding partition array A176723.
%C Row sums coincide with those of array A176723 for n>=1, and they are given by A007294.
%C If for n=0 a 1 is added (the empty partition defines the empty multiset class) the tabl structure will be lost.
%H W. Lang: <a href="/A176724/a176724.txt">First 15 rows and row sums.</a>
%F a(n,m) is the number of m part partitions of n which define m-multiset repetition classes. Multiset repetition class defining is equivalent to the following constraint on the exponents of a partition (1^e[1],2^e[2],...,M^e[M]):
%F e[1] >= e[2]>=...>=e[M]>=1, i.e., positive nonincreasing with largest part M. This will satisfy T(M) <= n where T(M) = A000217(M) are the triangular numbers; for each n every sufficiently small positive M does occur.
%e 1;
%e 0,1;
%e 0,1,1;
%e 0,0,1,1;
%e 0,0,0,1,1;
%e 0,0,1,1,1,1;
%e 0,0,0,1,1,1,1;
%e ...
%Y a(7,5)=1 because there is only one 5 part partition of 7 which is 5-multiset repetition class defining, namely (1^3,2^2) (see row n=7 of the partition array A176723). This defines the 5-multiset class representative {1,1,1,2,2}.
%K nonn,easy,tabl
%O 1,42
%A _Wolfdieter Lang_, Jul 14 2010
%E Edited (in response to comments by _Franklin T. Adams-Watters_) by _Wolfdieter Lang_, Apr 02 2011
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