Search: id:A058694
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%I A058694
%S A058694 1,1,2,6,30,210,2310,34650,762300,22869000,960498000,53787888000,
%T A058694 4141667376000,418308404976000,56471634671760000,9939007702229760000,
%U A058694 2295910779215074560000,681885501426877144320000,262525918049347700563200000
%N A058694 Partial products p(0)*p(1)*...*p(n) of partition numbers A000041.
%C A058694 a(n) gives the number of partitions P(V(n)) of V(n)=[1,2,3,...,n]. A 
               partition P(V(n)) acts on the components of V(n), i.e. the components 
               of V(n) are partitioned. Therefore a(n) results as the product of 
               the number of partitions P(i) of the component v(i)=i with i=1,...,
               n. For example, a(3) = 6 because we have 6 list partitions for the 
               list V(n=3)=[1,2,3]: [[1], [1, 1], [2, 1]], [[1], [1, 1], [1, 1, 
               1]], [[1], [1, 1], [3]], [[1], [2], [2, 1]], [[1], [2], [1, 1, 1]], 
               [[1], [2], [3]]. - Thomas Wieder (thomas.wieder(AT)t-online.de), 
               Sep 29 2007
%t A058694 Table[Product[PartitionsP[k], {k, 1, n}], {n, 1, 33}] [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Dec 13 2008]
%Y A058694 Cf. A000041, A000070.
%Y A058694 Sequence in context: A002110 A118491 A088257 this_sequence A046853 A136351 
               A071290
%Y A058694 Adjacent sequences: A058691 A058692 A058693 this_sequence A058695 A058696 
               A058697
%K A058694 nonn
%O A058694 0,3
%A A058694 N. J. A. Sloane (njas(AT)research.att.com), Dec 30 2000

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