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 A188490 Exponential transform of A003024, number of acyclic digraphs with n labeled nodes. 1

%I

%S 1,1,2,10,146,6010,636428,163326124,98126803670,134925234752998,

%T 417644922244986812,2873459543869519132876,43497844823465975411261876,

%U 1436705096446765490152625035300,102817732537500055044863771641124696

%N Exponential transform of A003024, number of acyclic digraphs with n labeled nodes.

%F G.f.: A(x) = exp( Sum_{n>=1} A003024(n)*x^n/n ) where A003024(n) is the number of acyclic digraphs with n labeled nodes.

%e G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 146*x^4 + 6010*x^5 +...

%e log(A(x)) = x + 3*x^2/2 + 25*x^3/3 + 543*x^4/4 + 29281*x^5/5 + 3781503*x^6/6 +...+ A003024(n)*x^n/n +...

%o (PARI) {A003024(n)=polcoeff(1-sum(k=0, n-1, A003024(k)*x^k/(1+2^k*x+x*O(x^n))^(k+1)), n)}

%o {a(n)=polcoeff(exp(sum(m=1,n,A003024(m)*x^m/m)+x*O(x^n)),n)}

%Y Cf. A003024 (log).

%K nonn

%O 0,3

%A _Paul D. Hanna_, Apr 01 2011

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Last modified September 23 02:26 EDT 2021. Contains 347609 sequences. (Running on oeis4.)