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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
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, 0, 0, 0, 2000, 11104, 33880, 73480, 123485, 166860, 184426, 167900, 125965, 77520, 38760, 15504, 4845, 1140, 190, 20, 1, 0, 0, 0, 0, 0, 41472, 337920, 1536000, 5062080 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..54.

R. J. Mathar, Statistics on Small Graphs, arXiv:1709.09000 (2017) Table 76.

FORMULA

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

EXAMPLE

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

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

0, 0, 0,   0,    0,     0, 1075648,...

MATHEMATICA

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 *)

CROSSREFS

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

Sequence in context: A057274 A088632 A057272 * A054547 A202717 A291195

Adjacent sequences:  A062732 A062733 A062734 * A062736 A062737 A062738

KEYWORD

easy,nonn,tabf

AUTHOR

Vladeta Jovovic, Jul 12 2001

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)