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%I #8 Mar 30 2012 18:37:34
%S 1,1,2,6,26,153,1230,13364,196940,3964902,110220876,4272079445,
%T 232593337728,17882578732969,1948605911230499,301712214427188701,
%U 66502429409739480660,20895237675211683912974,9368442364990639729658716,5998494566458610304486161295
%N G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/n * Product_{d|n} A(d*x^(n/d))^d ).
%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 26*x^4 + 153*x^5 + 1230*x^6 +...
%e By definition:
%e log(A(x)) = x*A(x) + x^2*A(x^2)*A(2*x)^2/2 + x^3*A(x^3)*A(3*x)^3/3 + x^4*A(x^4)*A(2*x^2)^2*A(4*x)^4/4 + x^5*A(x^5)*A(5*x)^5/5 + x^6*A(x^6)*A(2*x^3)^2*A(3*x^2)^3*A(6*x)^6/6 +...
%e Explicitly,
%e log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 79*x^4/4 + 616*x^5/5 + 6297*x^6/6 + 83518*x^7/7 + 1454615*x^8/8 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n+1,x^m/m*exp(sumdiv(m,d,log(subst(A^d,x,d*x^(m/d) +x*O(x^n))))))));polcoeff(A,n)}
%Y Cf. A205498, A205499, A205500, A205501.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 27 2012
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