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A119820 Coefficients of x^n in the n-th iteration of x*(1+x)^2 for n>=1. 7
1, 4, 27, 300, 4790, 101010, 2660028, 84191772, 3115739358, 132074618544, 6311492388432, 335744715016854, 19678501474466211, 1260060524755139120, 87519840721085385096, 6553840567691077634748, 526360263009035464610574 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

a(n) = [x^n] F_n(x) where F_n(x) = F_{n-1}(F_1(x)) with F_1(x) = x*(1+x)^2.

EXAMPLE

The successive iterations of F(x) = x*(1+x)^2 begin:

F(x) = (1)x + 2x^2 + x^3

F(F(x)) = x + (4)x^2 + 10x^3 + 18x^4 + 23x^5 + 22x^6 + 15x^7 + 6x^8 +...

F(F(F(x))) = x + 6x^2 + (27)x^3 + 102x^4 + 333x^5 + 960x^6 + 2472x^7 +...

F(F(F(F(x)))) = x + 8x^2 + 52x^3 + (300)x^4 + 1578x^5 + 7692x^6 +...

F(F(F(F(F(x))))) = x + 10x^2 + 85x^3 + 660x^4 + (4790)x^5 + 32920x^6+...

F(F(F(F(F(F(x)))))) = x + 12x^2 +126x^3 +1230x^4+11385x^5+(101010)x^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, G=subst(F, x, G)); return(polcoeff(G, n, x)))}

CROSSREFS

Cf. A119821, A112317, A119819, A119817, A119815.

Sequence in context: A179494 A295255 A203157 * A159599 A221411 A203202

Adjacent sequences:  A119817 A119818 A119819 * A119821 A119822 A119823

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 01 2006

STATUS

approved

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Last modified February 23 13:36 EST 2018. Contains 299581 sequences. (Running on oeis4.)