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%I #6 May 18 2020 04:45:54
%S 1,1,1,4,8,4,64,192,192,64,4096,16384,24576,16384,4096,1048576,
%T 5242880,10485760,10485760,5242880,1048576,1073741824,6442450944,
%U 16106127360,21474836480,16106127360,6442450944,1073741824,4398046511104,30786325577728,92358976733184,153931627888640,153931627888640,92358976733184,30786325577728,4398046511104
%N Triangular array read by rows. T(n,k) is the number of labeled digraphs on n nodes with exactly k self loops, n>=0, 0<=k<=n.
%F E.g.f.: g(x + y*x) where g(x) is the e.g.f. for A053763.
%e 1,
%e 1, 1,
%e 4, 8, 4,
%e 64, 192, 192, 64,
%e 4096, 16384, 24576, 16384, 4096
%t nn = 5; g[x_] := Sum[2^(n^2 - n) x^n/n!, {n, 0, nn}];Map[Select[#, # > 0 &] &,Range[0, nn]! CoefficientList[Series[g[ x + y x], {x, 0, nn}], {x, y}]] // Grid
%Y Cf. A053763 (column k=0), A002416 (row sums).
%K nonn,tabl
%O 0,4
%A _Geoffrey Critzer_, May 17 2020