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

1, 2, 10, 102, 1578, 32920, 864813, 27405798, 1017153322, 43271534196, 2075757894648, 110845691264880, 6521081183455941, 419050045344986432, 29204306270878653424, 2193909534863339799870, 176728502294889963614250

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Example

Coefficients in the initial iterations of F(x) = x*(1+x)^2 begin:
[(1),0,0,0,0,0,0,0,0,0,...];
[1,(2),1,0,0,0,0,0,0,0,...];
[1,4,(10),18,23,22,15,6,1,0,...];
[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),7178700,57976074,456783888,...];
[1,14,175,2058,23163,251832,2660028,(27405798),276215313,2729492562,...];
[1,16,232,3192,42308,544600,6842220,84191772,(1017153322),12088865688,...];
[1,18,297,4680,71388,1061712,15463512,221228244,3115739358,(43271534196),...];
where the terms enclosed in parenthesis form this sequence.
Some explicit expansions:
F(x) = x + (2)x^2 + x^3 ;
F(F(x)) = x + 4x^2 + (10)x^3 + 18x^4 + 23x^5 + 22x^6 + 15x^7 +...;
F(F(F(x))) = x + 6x^2 + 27x^3 + (102)x^4 + 333x^5 + 960x^6 +...;
F(F(F(F(x)))) = x + 8x^2 + 52x^3 + 300x^4 + (1578)x^5 + 7692x^6 +...;

Prog

(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)))}

Crossrefs

Cf. A119820.

Sequence in context: A342108 A135058 A346672 * A027270 A304319 A005799

Adjacent sequences: A154253 A154254 A154255 * A154257 A154258 A154259

Keyword

nonn

Author

Paul D. Hanna, Jan 05 2009

Status

approved