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%I #15 May 12 2019 18:05:17
%S 1,2,1,14,6,1,201,68,12,1,4704,1285,200,20,1,160890,36214,4815,460,30,
%T 1,7538040,1422288,160594,13755,910,42,1,462869190,74416131,7151984,
%U 535864,33110,1624,56,1,36055948320,5016901734,413347787,26821368,1490664,70686,2688,72,1,3474195588360
%N Triangle T(n,k) read by rows: number of labeled 2-regular digraphs (multiple arcs and loops allowed) on n nodes with k components.
%H E. N. Gilbert, <a href="https://doi.org/10.4153/CJM-1956-046-2">Enumeration of labelled graphs</a>, Can. J. Math. 8 (1956) 405-411.
%H Richard J. Mathar, <a href="https://arxiv.org/abs/1903.12477">2-regular Digraphs of the Lovelock Lagrangian</a>, arXiv:1903.12477 [math.GM], 2019.
%F T(n,1) = A123543(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!.
%F E.g.f.: sum_{n,k>=0} T(n,k)*x^n*t^k /n!= exp(t*E123543(x)) where E123543(x) = sum_{n>=1} A123543(n)*x^n/t^n. [Gilbert]. - _R. J. Mathar_, May 08 2019
%e The triangle starts:
%e 1;
%e 2,1;
%e 14,6,1;
%e 201,68,12,1;
%e 4704,1285,200,20,1;
%e 160890,36214,4815,460,30,1;
%e 7538040,1422288,160594,13755,910,42,1;
%Y Cf. A123543 (column k=1), A000681 (row sums).
%K nonn,tabl,easy
%O 1,2
%A _R. J. Mathar_, Apr 29 2019
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