OFFSET
1,5
EXAMPLE
Iterated compositions of [x + a(n)*x^n] forms F = x/(1-x):
x/(1-x) = 1x o x+1x^2 o x+1x^3 o x-1x^4 o x+3x^5 o x-3x^6 o x+6x^7 o x-15x^8 o x+58x^9 o x-64x^10 o x+198x^11 o x-476x^12 o...
The compositions get closer to F = x/(1-x) at each iteration:
(1) 1*x = x;
(2) 1*x o x+x^2 = x + x^2;
(3) 1*x o x+x^2 o x+1x^3 = x + x^2 + x^3 + 2*x^4 + x^6;
(4) 1*x o x+x^2 o x+1x^3 o x-1x^4 =
x + x^2 + x^3 + x^4 - 2*x^5 - 2*x^6 - 8*x^7 + x^8 - 3*x^9 +...
(5) 1*x o x+x^2 o x+1x^3 o x-1x^4 o x+3x^5 =
x + x^2 + x^3 + x^4 + x^5 + 4*x^6 + x^7 + 13*x^8 - 33*x^9 +...
(6) 1*x o x+x^2 o x+1x^3 o x-1x^4 o x+3x^5 o x-3x^6 =
x + x^2 + x^3 + x^4 + x^5 + x^6 - 5*x^7 + 4*x^8 - 45*x^9 +...
PROG
(PARI) {a(n)=local(F=x/(1-x+x*O(x^n)), G=x+x*O(x^n)); if(n<1, 0, if(n==1, polcoeff(F, 1), for(k=2, n, c=polcoeff(F/a(1), k)-polcoeff(G, k); G=subst(G, x, x+c*x^k); ); return(c)))}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 20 2006
STATUS
approved