A283417 - OEIS

%I #38 Aug 12 2020 18:56:20

%S 1,0,1,0,1,1,0,1,1,1,0,3,2,1,1,0,6,4,2,1,1,0,19,10,5,2,1,1,0,59,28,11,

%T 5,2,1,1,0,267,90,32,12,5,2,1,1,0,1380,363,100,33,12,5,2,1,1,0,9832,

%U 1784,397,104,34,12,5,2,1,1,0,90842,11770,1892,407,105,34,12,5,2,1,1

%N Number T(n,k) of triangle-free graphs on n unlabeled nodes with exactly k connected components; triangle T(n,k), n>=0, 0<=k<=n, read by rows.

%H Alois P. Heinz, <a href="/A283417/b283417.txt">Rows n = 0..17, flattened</a>

%H <a href="/index/Mu#multiplicative_completely">Index entries for triangles generated by the Multiset Transformation</a>

%F G.f.: Product_{j>=1} 1/(1-y*x^j)^A024607(j).

%e Triangle T(n,k) begins:

%e   1;

%e   0,    1;

%e   0,    1,    1;

%e   0,    1,    1,   1;

%e   0,    3,    2,   1,   1;

%e   0,    6,    4,   2,   1,  1;

%e   0,   19,   10,   5,   2,  1,  1;

%e   0,   59,   28,  11,   5,  2,  1, 1;

%e   0,  267,   90,  32,  12,  5,  2, 1, 1;

%e   0, 1380,  363, 100,  33, 12,  5, 2, 1, 1;

%e   0, 9832, 1784, 397, 104, 34, 12, 5, 2, 1, 1;

%e   ...

%Y Columns k=0-1 give: A000007, A024607.

%Y Row sums give A006785.

%K nonn,tabl

%O 0,12

%A _Alois P. Heinz_, Apr 14 2017