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A307806 Triangle T(n,k) read by rows: number of series-reduced labeled graphs on n nodes with k components. 1

%I

%S 1,1,1,0,3,1,5,3,6,1,51,25,15,10,1,3634,381,90,45,15,1,374119,26509,

%T 1596,280,105,21,1,73161880,3095579,111370,5061,770,210,28,1,

%U 26545249985,671957334,14411205,353262,13671,1890,378,36,1

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

%F T(n,1) = A003515(n).

%F 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 The triangle starts

%e 1;

%e 1,1;

%e 0,3,1;

%e 5,3,6,1;

%e 51,25,15,10,1;

%e 3634,381,90,45,15,1;

%e 374119,26509,1596,280,105,21,1;

%e 73161880,3095579,111370,5061,770,210,28,1;

%e 26545249985,671957334,14411205,353262,13671,1890,378,36,1;

%Y Cf. A003515 (column k=1), A003514 (row sums).

%K nonn,tabl,easy

%O 1,5

%A _R. J. Mathar_, Apr 29 2019

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Last modified March 31 16:23 EDT 2020. Contains 333151 sequences. (Running on oeis4.)