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A154256 Coefficients of x^n in the (n-1)-th iterations of x*(1+x)^2 for n>=1.

%I A154256 #4 Sep 13 2013 19:06:25
%S A154256 1,2,10,102,1578,32920,864813,27405798,1017153322,43271534196,
%T A154256 2075757894648,110845691264880,6521081183455941,419050045344986432,
%U A154256 29204306270878653424,2193909534863339799870,176728502294889963614250
%N A154256 Coefficients of x^n in the (n-1)-th iterations of x*(1+x)^2 for n>=1.
%e A154256 Coefficients in the initial iterations of F(x) = x*(1+x)^2 begin:
%e A154256 [(1),0,0,0,0,0,0,0,0,0,...];
%e A154256 [1,(2),1,0,0,0,0,0,0,0,...];
%e A154256 [1,4,(10),18,23,22,15,6,1,0,...];
%e A154256 [1,6,27,(102),333,960,2472,5748,12150,23388,...];
%e A154256 [1,8,52,300,(1578),7692,35094,150978,615939,2393628,...];
%e A154256 [1,10,85,660,4790,(32920),215988,1360638,8265613,48585702,...];
%e A154256 [1,12,126,1230,11385,101010,(864813),7178700,57976074,456783888,...];
%e A154256 [1,14,175,2058,23163,251832,2660028,(27405798),276215313,2729492562,...];
%e A154256 [1,16,232,3192,42308,544600,6842220,84191772,(1017153322),12088865688,...];
%e A154256 [1,18,297,4680,71388,1061712,15463512,221228244,3115739358,(43271534196),...];
%e A154256 where the terms enclosed in parenthesis form this sequence.
%e A154256 Some explicit expansions:
%e A154256 F(x) = x + (2)x^2 + x^3 ;
%e A154256 F(F(x)) = x + 4x^2 + (10)x^3 + 18x^4 + 23x^5 + 22x^6 + 15x^7 +...;
%e A154256 F(F(F(x))) = x + 6x^2 + 27x^3 + (102)x^4 + 333x^5 + 960x^6 +...;
%e A154256 F(F(F(F(x)))) = x + 8x^2 + 52x^3 + 300x^4 + (1578)x^5 + 7692x^6 +...;
%o A154256 (PARI) {a(n)=local(F=x*(1+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)))}
%Y A154256 Cf. A119820.
%K A154256 nonn
%O A154256 1,2
%A A154256 _Paul D. Hanna_, Jan 05 2009