Search: id:A079144
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%I A079144
%S A079144 1,3,19,207,3451,81663,2602699,107477247,5581680571,356046745023,
%T A079144 27365431508779,2494237642655487,266005087863259291,
%U A079144 32815976815540917183,4636895313201764853259,743988605732990946684927
%N A079144 Number of labeled interval orders on n elements: (2+2)-free posets.
%D A079144 D. Zagier, Vassiliev invariants and a strange identity related to the 
               Dedekind eta-function, Topology 40(5) (2001), 945-960.
%F A079144 1/(24^n)*sum(binomial(n, k)*A002439(k), k=0..n). Zagier 2001, p. 954.
%F A079144 G.f.: Sum(Product(1-exp(-k*x),k = 1 .. n),n = 0 .. infinity). a(n) = 
               Sum_{k=0..n} k!*Stirling2(n,k)*A138265(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Mar 11 2008
%F A079144 Contribution from Peter Bala (pbala(AT)talktalk.net), Mar 19 2009: (Start)
%F A079144 Conjectural form for the o.g.f. as a continued fraction:
%F A079144 1/(1-x/(1-2*x/(1-5*x/(1-7*x/(1-12*x/(1-15*x/(1- ...))))))) = 1 + x + 
               3*x^2 + 19*x^3 + 207*x^4 + ..., where the sequence [1,2,5,7,12,15,
               ..] is the sequence of generalised pentagonal numbers A001318. Compare 
               with the continued fraction form of the o.g.f. of A002105. (End)
%Y A079144 Cf. A022493 (unlabeled interval orders), A002439 (Glaisher's T numbers).
%Y A079144 Sequence in context: A027546 A108993 A052886 this_sequence A049056 A165356 
               A000275
%Y A079144 Adjacent sequences: A079141 A079142 A079143 this_sequence A079145 A079146 
               A079147
%K A079144 nonn,easy
%O A079144 1,2
%A A079144 Detlef Pauly (dettodet(AT)yahoo.de), Dec 27 2002

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