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A217563 Irregular triangular array read by rows. T(n,k) is the number of weakly connected relations on n labeled nodes with k arcs. (n>=0, 0<=k<=n^2).

%I A217563 #20 Jun 02 2025 08:09:57
%S A217563 1,1,1,0,2,5,4,1,0,0,12,56,111,123,84,36,9,1,0,0,0,128,944,3264,7096,
%T A217563 10936,12687,11400,8004,4368,1820,560,120,16,1,0,0,0,0,2000,21104,
%U A217563 109400,373920,950725,1915405,3168880,4394760,5169230,5188390,4454000
%N A217563 Irregular triangular array read by rows. T(n,k)  is the number of weakly connected relations on n labeled nodes with k arcs. (n>=0, 0<=k<=n^2).
%C A217563 Row sums = A062738.
%F A217563 E.g.f.: Log[Sum_{n>=0} (1+y)^(n^2) x^n/n!] + 1
%e A217563 1,
%e A217563 1, 1,
%e A217563 0, 2, 5, 4, 1,
%e A217563 0, 0, 12, 56, 111, 123, 84, 36, 9, 1,
%e A217563 0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1
%t A217563 nn=6; s=Sum[(1+y)^(n^2) x^n/n!, {n,0,nn}]; Range[0,nn]! CoefficientList[Series[ Log[s]+1, {x,0,nn}], {x,y}] //Grid
%Y A217563 Cf. A062735.
%K A217563 nonn,tabf
%O A217563 0,5
%A A217563 _Geoffrey Critzer_, Oct 07 2012