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A054914 Number of labeled connected digraphs with n nodes such that complement is also connected. 1

%I

%S 1,2,44,3572,1005584,1060875152,4382913876704,71987098738435232,

%T 4721068803628864289024,1237845578934919489219757312,

%U 1298046978912816702510086132201984,5444486716626952189940499391640815580672,91343710775311761525117954724021374685703481344

%N Number of labeled connected digraphs with n nodes such that complement is also connected.

%H Alois P. Heinz, <a href="/A054914/b054914.txt">Table of n, a(n) for n = 1..50</a>

%H V. A. Liskovets, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LISK/Derseq.html">Some easily derivable sequences</a>, J. Integer Sequences, 3 (2000), #00.2.2.

%F a(n) = 2*A003027(n) - A053763(n).

%p b:= n-> 2^(n^2-n):

%p g:= proc(n) option remember; local k; `if`(n=0, 1,

%p b(n)- add(k*binomial(n,k) *b(n-k)*g(k), k=1..n-1)/n)

%p end:

%p a:= n-> 2*g(n)-b(n):

%p seq (a(n), n=1..20); # _Alois P. Heinz_, Oct 21 2012

%t nn=20;g=Sum[2^(2Binomial[n,2])x^n/n!,{n,0,nn}];Drop[Range[0,nn]!CoefficientList[Series[2(Log[g]+1)-g,{x,0,nn}],x],1] (* _Geoffrey Critzer_, Oct 21 2012 *)

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, May 23 2000

%E More terms from _Vladeta Jovovic_, Jul 17 2000

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)