%I A066855
%S A066855 1,1,1,1,1,1,2,2,1,1,1,3,2,1,1,2,4,4,2,1,1,1,5,5,4,2,1,1,3,7,8,6,4,2,1,
%T A066855 1,2,8,11,9,6,4,2,1,1,2,11,16,14,10,6,4,2,1,1,1,11,20,20,15,10,6,4,2,1,
%U A066855 1,4,15,28,29,23,16,10,6,4,2,1,1,1,16,33,39,33,24,16,10,6,4,2,1,1,2,19
%N A066855 Triangle T(n,k) of numbers of representations of n as a sum of k products 
               of positive integers, k=1..n. 1 is not allowed as a factor, unless 
               it is the only factor.Representations which differ only in the order 
               of terms or factors are considered equivalent.
%C A066855 Row sums give A066739.
%F A066855 G.f.: Product_{m=1..infinity} (1-y*x^m)^(-A001055(m)). T(n, k) = Sum_{pi} 
               Product_{m=1..n} binomial(p(m)+A001055(m)-1, p(m)), where pi runs 
               through all nonnegative solutions of p(1)+2*p(2)+...+n*p(n)=n, p(1)+p(2)+...+p(n)=k.
%e A066855 [1], [1, 1], [1, 1, 1], [2, 2, 1, 1], [1, 3, 2, 1, 1], ... . For n=5, 
               5 = 4+1 = 2*2+1 = 3+2 = 3+1+1 = 2+2+1 = 2+1+1+1 = 1+1+1+1+1, giving 
               the batch [1, 3, 2, 1, 1].
%Y A066855 Cf. A001055, A066739.
%Y A066855 Sequence in context: A112465 A112468 A086275 this_sequence A058914 A123682 
               A134513
%Y A066855 Adjacent sequences: A066852 A066853 A066854 this_sequence A066856 A066857 
               A066858
%K A066855 nonn,tabl
%O A066855 1,7
%A A066855 Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 21 2002