login
Expansion of f(f(x)), where f = x + x^2 + x^4 + x^8 + x^16 + ...
1

%I #28 Mar 20 2020 19:15:18

%S 1,2,2,3,6,8,8,16,22,40,80,146,240,356,488,661,870,1184,1936,3750,

%T 7976,17628,37528,74828,140480,249444,420392,678432,1056600,1593512,

%U 2334928,3337410,4660246,6364080,8527984,11258182,14753032,19622940,27836440

%N Expansion of f(f(x)), where f = x + x^2 + x^4 + x^8 + x^16 + ...

%H Robert Israel, <a href="/A007801/b007801.txt">Table of n, a(n) for n = 1..1023</a>

%F a(n) = Sum_{k=1..n} A073266(n,k)*f(k). - _Vladimir Kruchinin_, Mar 13 2012

%p e:= 8;

%p f:= x -> sum(x^(2^i),i=0..e):

%p g:= f(f(x)):

%p S:= series(g,x,2^e):

%p seq(coeff(S,x,n),n=0..2^e-1); # _Robert Israel_, Aug 19 2014

%t f[x_]:= Sum[x^(2^j), {j,0,10}]; g[x_]:=f[f[x]]; CoefficientList[Series[g[x], {x, 0, 50}], x] (* _G. C. Greubel_, Mar 05 2020 *)

%K nonn

%O 1,2

%A _Jeffrey Shallit_