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A062735 Triangular array T(n,k) giving number of weakly connected digraphs with n labeled nodes and k arcs (n >= 1, 0 <= k <= n(n-1)). 2

%I

%S 1,0,2,1,0,0,12,20,15,6,1,0,0,0,128,432,768,920,792,495,220,66,12,1,0,

%T 0,0,0,2000,11104,33880,73480,123485,166860,184426,167900,125965,

%U 77520,38760,15504,4845,1140,190,20,1,0,0,0,0,0,41472,337920,1536000,5062080

%N Triangular array T(n,k) giving number of weakly connected digraphs with n labeled nodes and k arcs (n >= 1, 0 <= k <= n(n-1)).

%H R. J. Mathar, <a href="http://arxiv.org/abs/1709.09000">Statistics on Small Graphs</a>, arXiv:1709.09000 (2017) Table 76.

%F E.g.f.: 1+log( Sum_{n >= 0, k >= 0} binomial(n*(n-1), k)*x^n/n!*y^k ).

%e 1;

%e 0, 2, 1;

%e 0, 0, 12, 20, 15, 6, 1;

%e 0, 0, 0, 128, 432, 768, 920, 792, 495, 220, 66, 12, 1;

%e 0, 0, 0, 0, 2000, 11104, 33880, 73480, 123485, 166860, 184426, 167900, ...;

%e 0, 0, 0, 0, 0, 41472, 337920,1536000,5062080,.. ;

%e 0, 0, 0, 0, 0, 0, 1075648,...

%t nn=7;s=Sum[(1+y)^(n^2-n) x^n/n!,{n,0,nn}];Range[0,nn]!CoefficientList[Series[Log[ s]+1,{x,0,nn}],{x,y}]//Grid (* returns triangle indexed from n = 0, _Geoffrey Critzer_, Oct 07 2012 *)

%Y Cf. (row sums) A003027, (unlabeled case) A054733, diagonal (A097629).

%K easy,nonn,tabf

%O 1,3

%A _Vladeta Jovovic_, Jul 12 2001

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)