A007801 Expansion of f(f(x)), where f = x + x^2 + x^4 + x^8 + x^16 + ...

1, 2, 2, 3, 6, 8, 8, 16, 22, 40, 80, 146, 240, 356, 488, 661, 870, 1184, 1936, 3750, 7976, 17628, 37528, 74828, 140480, 249444, 420392, 678432, 1056600, 1593512, 2334928, 3337410, 4660246, 6364080, 8527984, 11258182, 14753032, 19622940, 27836440

Offset: 1

Author

Jeffrey Shallit

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..1023

Programs

Maple

e:= 8;
f:= x -> sum(x^(2^i),i=0..e):
g:= f(f(x)):
S:= series(g,x,2^e):
seq(coeff(S,x,n),n=0..2^e-1); # Robert Israel, Aug 19 2014

Mathematica

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 *)

Formula

a(n) = Sum_{k=1..n} A073266(n,k)*f(k). - Vladimir Kruchinin, Mar 13 2012