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%I #17 Feb 10 2015 17:30:56
%S 1,1,2,9,64,630,7916,121023,2179556,45179508,1059312264,27715541568,
%T 800423573676,25289923553700,867723362137464,32128443862364255,
%U 1276818947065793736,54208515369076658640,2448636361058495090816,117254071399557173396416
%N Coefficients of x^n in the (n-1)-th iteration of (x + x^2) for n>=1.
%H Paul D. Hanna, <a href="/A112319/b112319.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = [x^n] F_{n-1}(x) where F_n(x) = F_{n-1}(x+x^2) with F_1(x) = x+x^2 and F_0(x)=x for n>=1.
%e The iterations of (x+x^2) begin:
%e F(x) = x + (1)*x^2
%e F(F(x)) = x + 2*x^2 + (2)*x^3 + x^4
%e F(F(F(x))) = x + 3*x^2 + 6*x^3+ (9)*x^4 +...
%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 + (630)*x^6 +...
%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=1,30,print1(a(n),", "))
%Y Cf. A112317, A112320.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Sep 06 2005
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