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%I #2 Mar 30 2012 18:37:18
%S 1,6,52,660,11385,251832,6842220,221228244,8311401351,356190316416,
%T 17160064580802,918453056609946,54085054802995008,3475794779752572784,
%U 242103490865991893116,18170143514998451547348
%N Coefficients of x^n in the (n+1)-th iteration of x*(1+x)^2 for n>=1.
%e Coefficients in the initial iterations of x*(1+x)^2 begin:
%e [1,2,1];
%e [(1),4,10,18,23,22,15,6,1];
%e [1,(6),27,102,333,960,2472,5748,12150,23388,...];
%e [1,8,(52),300,1578,7692,35094,150978,615939,2393628,...];
%e [1,10,85,(660),4790,32920,215988,1360638,8265613,48585702,...];
%e [1,12,126,1230,(11385),101010,864813,7178700,57976074,...];
%e [1,14,175,2058,23163,(251832),2660028,27405798,276215313,...];
%e [1,16,232,3192,42308,544600,(6842220),84191772,1017153322,...];
%e [1,18,297,4680,71388,1061712,15463512,(221228244),3115739358,...];
%e [1,20,370,6570,113355,1912590,31683051,516686346,(8311401351),...]; ...
%e where the coefficients in parenthesis form the initial terms of this sequence.
%o (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 Cf. A166888, A154256, A119820, A166890.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Nov 22 2009
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