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A307806 Triangle T(n,k) read by rows: number of series-reduced labeled graphs on n nodes with k components.

%I A307806 #7 Apr 29 2019 17:24:57
%S A307806 1,1,1,0,3,1,5,3,6,1,51,25,15,10,1,3634,381,90,45,15,1,374119,26509,
%T A307806 1596,280,105,21,1,73161880,3095579,111370,5061,770,210,28,1,
%U A307806 26545249985,671957334,14411205,353262,13671,1890,378,36,1
%N A307806 Triangle T(n,k) read by rows: number of series-reduced labeled graphs on n nodes with k components.
%F A307806 T(n,1) = A003515(n).
%F A307806 T(n,k) = Sum_{Compositions n=n_1+n_2+...n_k, n_i>=1} multinomial(n; n_1,n_2,..,n_k) * T(n_1,1) * T(n_2,1) *... T(n_k,1)/ k!.
%e A307806 The triangle starts
%e A307806 1;
%e A307806 1,1;
%e A307806 0,3,1;
%e A307806 5,3,6,1;
%e A307806 51,25,15,10,1;
%e A307806 3634,381,90,45,15,1;
%e A307806 374119,26509,1596,280,105,21,1;
%e A307806 73161880,3095579,111370,5061,770,210,28,1;
%e A307806 26545249985,671957334,14411205,353262,13671,1890,378,36,1;
%Y A307806 Cf. A003515 (column k=1), A003514 (row sums).
%K A307806 nonn,tabl,easy
%O A307806 1,5
%A A307806 _R. J. Mathar_, Apr 29 2019