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a(n) is the number of ways to split the set {1,2,...,n} into two disjoint subsets S,T with S union T = {1,2,...,n} and linearly order S and then choose a subset of T. - Geoffrey Critzer, Mar 10 2009
a(n) is the number of ways to split the set {1,2,...,n} into two disjoint subsets S,T with S union T = {1,2,...,n} and linearly order S and then choose a subset of T. - Geoffrey Critzer, Mar 10 2009
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a(n) = F(n), where the function F(x) := 2^(1+x+1) * Integral_{t >= 0..oo} e^(-2*ut)*(1 + ut)^x du dt smoothly interpolates this sequence to all real values of x. - Peter Bala, Sep 05 2023
G.f.: A(x) = 1/(1 - 2*x - x/(1 - x/(1 - 2*x - 2*x/(1 - 2*x/(1 - 2*x - 3*x/(1 - 3*x/(1 - 2*x - 4*x/(1 - 4*x/(1 - 2*x - p... ))))))))). - Peter Bala, May 26 2017
a(n) = F(n), where the function F(x) := 2^(1+x) * Integral_{0..oo} e^(-2*u)*(1 + u)^x du smoothly interpolates this sequence to all real values of x. - Peter Bala, Sep 05 2023
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(MAGMAMagma) m:=45; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(2*x)/(1-x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Oct 16 2018
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