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A176724 Triangle for number of partitions which define multiset repetition classes.

%I A176724 #15 Aug 29 2019 17:19:28
%S A176724 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 A176724 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 A176724 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 A176724 Triangle for number of partitions which define multiset repetition classes.
%C A176724 For definitions, references, links and examples see the corresponding partition array A176723.
%C A176724 Row sums coincide with those of array A176723 for n>=1, and they are given by A007294.
%C A176724 If for n=0 a 1 is added (the empty partition defines the empty multiset class) the tabl structure will be lost.
%H A176724 W. Lang: <a href="/A176724/a176724.txt">First 15 rows and row sums.</a>
%F A176724 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 A176724   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 A176724 1;
%e A176724 0,1;
%e A176724 0,1,1;
%e A176724 0,0,1,1;
%e A176724 0,0,0,1,1;
%e A176724 0,0,1,1,1,1;
%e A176724 0,0,0,1,1,1,1;
%e A176724 ...
%Y A176724 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 A176724 nonn,easy,tabl
%O A176724 1,42
%A A176724 _Wolfdieter Lang_, Jul 14 2010
%E A176724 Edited (in response to comments by _Franklin T. Adams-Watters_) by _Wolfdieter Lang_, Apr 02 2011