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A062738 Number of connected labeled relations. 10
1, 2, 12, 432, 61344, 32866560, 68307743232, 561981464819712, 18437720675374485504, 2417519433343618432696320, 1267602236528793479228867346432, 2658428102191640176274135259655176192, 22300681394917309655766001890404571062206464 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

FORMULA

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

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 *)

PROG

(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

CROSSREFS

Cf. A003027.

Sequence in context: A012428 A012786 A168504 * A296623 A009510 A091471

Adjacent sequences:  A062735 A062736 A062737 * A062739 A062740 A062741

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Jul 12 2001

STATUS

approved

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)