A166889 Coefficients of x^n in the (n+1)-th iteration of x*(1+x)^2 for n>=1.

1, 6, 52, 660, 11385, 251832, 6842220, 221228244, 8311401351, 356190316416, 17160064580802, 918453056609946, 54085054802995008, 3475794779752572784, 242103490865991893116, 18170143514998451547348

Offset: 1

Author

Paul D. Hanna, Nov 22 2009

Keywords

• nonn

Examples

			Coefficients in the initial iterations of x*(1+x)^2 begin:
[1,2,1];
[(1),4,10,18,23,22,15,6,1];
[1,(6),27,102,333,960,2472,5748,12150,23388,...];
[1,8,(52),300,1578,7692,35094,150978,615939,2393628,...];
[1,10,85,(660),4790,32920,215988,1360638,8265613,48585702,...];
[1,12,126,1230,(11385),101010,864813,7178700,57976074,...];
[1,14,175,2058,23163,(251832),2660028,27405798,276215313,...];
[1,16,232,3192,42308,544600,(6842220),84191772,1017153322,...];
[1,18,297,4680,71388,1061712,15463512,(221228244),3115739358,...];
[1,20,370,6570,113355,1912590,31683051,516686346,(8311401351),...]; ...
where the coefficients in parenthesis form the initial terms of this sequence.
		

Crossrefs

Cf. A166888, A154256, A119820, A166890.

Programs

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)))}