%I A058843
%S A058843 1,1,2,1,12,8,1,80,192,64,1,720,5120,5120,1024,1,9152,192000,450560,
%T A058843 245760,32768,1,165312,10938368,56197120,64225280,22020096,2097152,
%U A058843 1,4244480,976453632,10877927424,23781703680,15971909632,3758096384
%N A058843 Triangle T(n,k) = C_n(k) where C_n(k) = number of k-colored labeled graphs 
               with n nodes (n >= 1, 1<=k<=n).
%D A058843 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 18, Table 1.5.1.
%F A058843 C_n(k) = Sum_{i=1..n-1} binomial(n, i)*2^(i*(n-i))*C_i(k-1)/k.
%e A058843 1; 1,2; 1,12,8; 1,80,192,64; ...
%p A058843 for p from 1 to 20 do C[p,1] := 1; od: for k from 2 to 20 do for p from 
               1 to k-1 do C[p,k] := 0; od: od: for k from 2 to 10 do for p from 
               k to 10 do C[p,k] := add( binomial(p,n)*2^(n*(p-n))*C[n,k-1]/k,n=1..p-1); 
               od: od:
%Y A058843 Apart from scaling, same as A058875. Columns give A058872 and A000683, 
               A058873 and A006201, A058874 and A006202, also A006218.
%Y A058843 Sequence in context: A085752 A074966 A128413 this_sequence A130559 A135256 
               A090586
%Y A058843 Adjacent sequences: A058840 A058841 A058842 this_sequence A058844 A058845 
               A058846
%K A058843 nonn,easy,tabl
%O A058843 1,3
%A A058843 N. J. A. Sloane (njas(AT)research.att.com), Jan 07 2001