Search: id:A106235
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%I A106235
%S A106235 0,1,0,2,0,0,4,1,0,0,9,2,0,0,0,20,7,1,0,0,0,48,17,2,0,0,0,0,115,48,7,1,
%T A106235 0,0,0,0,286,124,21,2,0,0,0,0,0,719,336,60,7,1,0,0,0,0,0,1842,888,171,
%U A106235 21,2,0,0,0,0,0,0,4766,2393,488,65,7,1,0,0
%N A106235 Triangle of the numbers of different forests of m rooted trees of smallest 
               order 2, i.e., without isolated vertices.
%C A106235 Forests of order N with m components, m>floor(N/2) must contain an isolated 
               vertex since it is impossible to partition N vertices in floor(N/
               2) + 1 or more trees without give only one vertex to a tree. A033185(n) 
               = A106235(n) + A106234(n).
%F A106235 a(n)= sum over the partitions of N:1K1+2K2+ ... +NKN, with exactly m 
               parts and no part equal to 1, of product_{1=<i<=N}C(A000081(i)+Ki-1, 
               Ki).
%e A106235 a(12)=2 because 5 nodes can be partitioned in two trees only in a way: 
               one tree gets 3 nodes and the other tree gets 2. Since A000081(3) 
               = 2 and A000081(2)=1, there are two forests.
%Y A106235 Cf. A033185, A106234.
%Y A106235 Sequence in context: A061669 A136334 A155039 this_sequence A118965 A121552 
               A158118
%Y A106235 Adjacent sequences: A106232 A106233 A106234 this_sequence A106236 A106237 
               A106238
%K A106235 nonn,tabl
%O A106235 1,4
%A A106235 Washington Bomfim (webonfim(AT)bol.com.br), Apr 26 2005

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