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%I #7 Feb 10 2015 17:28:38
%S 1,3,12,70,560,5810,74760,1153740,20817588,430604724,10052947476,
%T 261595087182,7509722346204,235808741944100,8040824716606176,
%U 295914258931377276,11690732617035570008,493527339623630078552
%N Coefficient of x^n in the (n+1)-th iteration of (x + x^2) for n>=1.
%F a(n) = [x^n] F_{n+1}(x) where F_{n+1}(x) = F_n(x+x^2) with F_1(x) = x+x^2 and F_0(x)=x for n>=1.
%e The first few iterations of (x+x^2) begin:
%e F(x) = x + x^2;
%e F(F(x)) = (1)*x + 2*x^2 + 2*x^3 + x^4;
%e F(F(F(x))) = x + (3)*x^2 + 6*x^3 + 9*x^4 + 10*x^5 +...;
%e F(F(F(F(x)))) = x + 4*x^2 + (12)*x^3 + 30*x^4 + 64*x^5 +...;
%e F(F(F(F(F(x))))) = x + 5*x^2 + 20*x^3 + (70)*x^4 + 220*x^5 +...;
%e F(F(F(F(F(F(x)))))) = x + 6*x^2 + 30*x^3 + 135*x^4 + (560)*x^5 +...;
%e coefficients enclosed in parenthesis form the initial terms of this sequence.
%o (PARI) {a(n)=local(F=x+x^2, G=x+x*O(x^n));if(n<1,0, for(i=1,n+1,G=subst(F,x,G));return(polcoeff(G,n,x)))}
%o for(n=1,25,print1(a(n),", "))
%Y Cf. A112317, A112319.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Sep 06 2005
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