A119820 - OEIS

%I #5 Aug 27 2013 02:02:37

%S 1,4,27,300,4790,101010,2660028,84191772,3115739358,132074618544,

%T 6311492388432,335744715016854,19678501474466211,1260060524755139120,

%U 87519840721085385096,6553840567691077634748,526360263009035464610574

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

%F 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.

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

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

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

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

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

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

%e F(F(F(F(F(F(x)))))) = x + 12x^2 +126x^3 +1230x^4+11385x^5+(101010)x^6+...

%o (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)))}

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

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 01 2006