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A048287
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Number of semiorders on n labeled nodes whose incomparability graph is connected.
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8
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1, 1, 7, 61, 751, 11821, 226927, 5142061, 134341711, 3975839341, 131463171247, 4803293266861, 192178106208271, 8356430510670061, 392386967808249967, 19788154572706556461, 1066668756919315412431, 61204224384073232815981
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| E.g.f.: 1-2*(1-exp(-x))/(1-sqrt(4*exp(-x)-3)).
a(n) = Sum_{k=1..n} (-1)^(n-k)*Stirling2(n, k)*k!*Catalan(k-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 18 2003
Equals column 1 (unsigned) of triangle A136595, which is the matrix inverse of the triangle A136590 of trinomial logarithmic coefficients. - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 10 2008
E.g.f A(x)=F(exp(x)-1), F(x)=x*A005043(x). [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Sep 07 2010]
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EXAMPLE
| a(3)=7, the seven semiorders being three disjoint points and the disjoint union of a point and a two-element chain (with six labelings)
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PROG
| (PARI) {a(n)=local(A136590=matrix(n+1, n+1, r, c, if(r>=c, (r-1)!/(c-1)!*polcoeff(log(1+x+x^2 +x*O(x^n))^(c-1), r-1)))); (-1)^(n+1)*(A136590^-1)[n+1, 2]} - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 10 2008
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CROSSREFS
| Cf. A000108, A006531.
Cf. A136595, A136590.
Sequence in context: A061634 A049402 A001830 * A145507 A047685 A171078
Adjacent sequences: A048284 A048285 A048286 * A048288 A048289 A048290
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KEYWORD
| easy,nonn
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AUTHOR
| R. P. Stanley (rstan(AT)math.mit.edu)
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 18 2003
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