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%I #32 Apr 10 2019 04:46:24
%S 1,1,8,1,96,384,1,2048,36864,98304,1,84480,6881280,62914560,125829120,
%T 1,7221248,3043491840,80530636800,483183820800,773094113280,1,
%U 1218502656,3326443782144,260661565194240,3752083429785600,16624615811973120,22166154415964160,1,421846581248,9253226255745024,2290594981959696384,75808248102597427200,726340547902313594880,2542191917658097582080,2905362191609254379520
%N Triangular array read by rows. T(n,k) is the number of k-colored labeled digraphs with n vertices, n>=1, 1<=k<=n.
%C Here, a k-colored digraph is a digraph whose labels are colored with exactly k colors so that no two adjacent vertices have the same color.
%H Chris Ying, <a href="https://arxiv.org/abs/1902.06192">Enumerating Unique Computational Graphs via an Iterative Graph Invariant</a>, arXiv:1902.06192 [cs.DM], 2019.
%F T(n,k)= n!*2^(n^2)*[x^n] (A(x) - 1)^k where A(x)=Sum{n>=0}x^n/(n!*2^(n^2)).
%F T(n,n)= n!*2^(n^2-n).
%e 1,
%e 1, 8,
%e 1, 96, 384,
%e 1, 2048, 36864, 98304,
%e 1, 84480, 6881280, 62914560, 125829120,
%e 1, 7221248, 3043491840, 80530636800, 483183820800, 773094113280
%e T(2,2)=8 because there are 4 directed graphs on 4 labeled nodes and each is counted two times. 4*2=8.
%t nn=10;f[x_]:=Sum[x^n/(n!*2^(2*Binomial[n,2])),{n,0,nn}];Map[Select[#,#>0&]&,Drop[Transpose[Table[Table[n!*2^(2*Binomial[n,2]),{n,0,nn}]CoefficientList[Series[(f[x]-1)^k,{x,0,nn}],x],{k,1,nn}]],1]]//Grid
%K nonn,tabl
%O 1,3
%A _Geoffrey Critzer_, Aug 04 2014
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