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L.g.f: A(x) = Sum_{n>=1} a(n)*x^n/n = Sum_{n>=1} E( a(n)*x )^n*x^n/n where E(x) = exp(A(x)) is the g.f. of A180720.
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%I #2 Mar 30 2012 18:37:22

%S 1,3,16,183,6236,1057176,1733913028,74017764628367,

%T 352900886016894052282,1553933222263165003400252699258,

%U 133132594387470620595913152570240200262971699

%N L.g.f: A(x) = Sum_{n>=1} a(n)*x^n/n = Sum_{n>=1} E( a(n)*x )^n*x^n/n where E(x) = exp(A(x)) is the g.f. of A180720.

%e L.g.f: A(x) = x + 3*x^2/2 + 16*x^3/3 + 183*x^4/4 + 6236*x^5/5 +...+ a(n)*x^n/n +...

%e which also equals the series:

%e A(x) = log(E(x)) = E(x)*x + E(3*x)^2*x^2/2 + E(16*x)^3*x^3/3 + E(183*x)^4*x^4/4 + E(6236*x)^5*x^5/5 +...+ E(a(n)*x)^n*x^n/n +...

%e where E(x) is the integer series:

%e E(x) = 1 + x + 2*x^2 + 7*x^3 + 53*x^4 + 1305*x^5 + 177559*x^6 + 247880897*x^7 + 9252468642944*x^8 +...+ A180720(n)*x^n +...

%o (PARI) {a(n)=local(A=1+x+x*O(x^n),L);for(i=1,n,L=Vec(deriv(log(A))); A=exp(sum(m=1,#L,subst(A,x,L[m]*x)^m*x^m/m)+x*O(x^n)));if(n<1,0,L[n])}

%Y Cf. A180720.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 19 2010