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%I #7 Aug 06 2021 15:37:11
%S 2,5,16,59,244,1112,5516,29505,168938,1029271,6639768,45162696,
%T 322739878,2415567889,18884022724,153826198419,1302844673004,
%U 11451006297332,104262283711688,981877752182053,9550121928456718,95809651792320751,990221394289370920
%N Number of partitions of the (n+3)-multiset {0,0,0,1,2,...,n} into distinct multisets.
%C Also number of factorizations of 8 * Product_{i=1..n} prime(i+1) into distinct factors.
%H Alois P. Heinz, <a href="/A346813/b346813.txt">Table of n, a(n) for n = 0..573</a>
%Y Row n=3 of A346520.
%Y Cf. A169587.
%K nonn
%O 0,1
%A _Alois P. Heinz_, Aug 05 2021
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