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%I #3 Mar 30 2012 18:36:59
%S 1,1,4,17,106,796,7176,75057,894100,11946906,176939192,2876683340,
%T 50931297912,975391344376,20090039762944,442830738561585,
%U 10400937450758286,259318357362882148,6839990934297006668
%N L.g.f.: A(x) satisfies: A(x+x^2) = 2*A(x) - log(1+x) with A(0)=0; thus A(x) = log(B(x)), where B(x) is g.f. of A122938.
%C a(n) = n * Sum_{k=0..n-1} (-1)^(n-k-1)*A122941(n-k,k)/(n-k).
%F L.g.f.: A(x) = Sum_{n>=1} a(n)*x^n/n = Sum_{n>=0} log(1 + F_n(x))/2^(n+1) where F_0(x)=x, F_{n+1}(x) = F_n(x+x^2); a sum involving self-compositions of x+x^2 (cf. A122888).
%e To illustrate A(x+x^2) = 2*A(x) - log(1+x):
%e A(x) = x + 1*x^2/2 + 4*x^3/3 + 17*x^4/4 + 106*x^5/5 + 796*x^6/6 +...
%e A(x+x^2) = x + 3*x^2/2 + 7*x^3/3 + 35*x^4/4 + 211*x^5/5 + 1593*x^6/6 +...
%o (PARI) {a(n)=local(A=x+x*O(x^n)); for(i=0,n,A=-A+subst(A,x,x+x^2)+log(1+x+x*O(x^n)));n*polcoeff(A,n)}
%Y Cf. A122938; related tables: A122941, A122888.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Sep 25 2006
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