A062738 Number of connected labeled relations.

1, 2, 12, 432, 61344, 32866560, 68307743232, 561981464819712, 18437720675374485504, 2417519433343618432696320, 1267602236528793479228867346432, 2658428102191640176274135259655176192, 22300681394917309655766001890404571062206464

Offset: 0

Author

Vladeta Jovovic, Jul 12 2001

Keywords

• easy
• nonn

Comments

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.

Links

• T. D. Noe, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A003027.

Programs

Maple

a:= n-> n!*coeff(series(1+log(add(2^(i^2)*x^i/i!, i=0..n)), x, n+1), x, n):
seq(a(n), n=0..30); # Alois P. Heinz, Feb 16 2011

Mathematica

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 *)

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

Formula

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