%I #25 Aug 03 2014 14:29:46

%S 1,2,12,432,61344,32866560,68307743232,561981464819712,

%T 18437720675374485504,2417519433343618432696320,

%U 1267602236528793479228867346432,2658428102191640176274135259655176192,22300681394917309655766001890404571062206464

%N Number of connected labeled relations.

%C a(n) is the number of binary relations R on {1, 2, ..., n} such that the reflexive, symmetric, and transitive closure of R is the trivial relation.

%H T. D. Noe, <a href="/A062738/b062738.txt">Table of n, a(n) for n = 0..30</a>

%F E.g.f.: 1+log( Sum_{n >= 0} 2^(n^2)*x^n/n! ).

%p a:= n-> n!*coeff(series(1+log(add(2^(i^2)*x^i/i!, i=0..n)), x, n+1), x, n):

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Feb 16 2011

%t nn = 20; a = Sum[2^(n^2) x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[Log[a] + 1, {x, 0, nn}], x] (* _Geoffrey Critzer_, Oct 17 2011 *)

%o (PARI) v=Vec(1+log(sum(n=0,10,2^(n^2)*x^n/n!)));for(i=1,#v,v[i]*=(i-1)!);v \\ _Charles R Greathouse IV_, Feb 14 2011

%Y Cf. A003027.

%K easy,nonn

%O 0,2

%A _Vladeta Jovovic_, Jul 12 2001