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A062738
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Number of connected labeled relations.
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7
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1, 2, 12, 432, 61344, 32866560, 68307743232, 561981464819712, 18437720675374485504, 2417519433343618432696320, 1267602236528793479228867346432, 2658428102191640176274135259655176192
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..30
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FORMULA
| E.g.f.: 1+log( Sum_{n >= 0} 2^(n^2)*x^n/n! ).
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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
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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 *)
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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
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CROSSREFS
| Cf. A003027.
Sequence in context: A012428 A012786 A168504 * A009510 A091471 A012625
Adjacent sequences: A062735 A062736 A062737 * A062739 A062740 A062741
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 12 2001
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