A119459 - OEIS

%I #3 Mar 30 2012 18:36:57

%S 1,-1,1,2,6,10,27,54,253,312,1116,2194,6157,15552,54514,89014,687252,

%T 964080,2577597,6822210,22066744,38505658,119635413,289026266,

%U 517893326,2410443144,9800259872,22806899334,87955801599,189512770532,416815519198,1126216162158,9805754835374

%N Decomposition of function F = x/(1-x) into functions of the form [x + a(n)*x^n]: x = ...o x+a(n)*x^n o...o x+a(3)*x^3 o x+a(2)*x^2 o a(1)*x o F.

%e Iterated decompositions of F=x/(1-x) into [x + a(n)*x^n]:

%e x = ... o x+6*x^5 o x+2*x^4 o x+1*x^3 o x-1*x^2 o 1*x o F.

%e These decompositions get closer to x at each iteration:

%e (1) 1*x o F = x/(1-x) = x + x^2 + x^3 + x^4 + x^5 +...

%e (2) x-1*x^2 o 1*x o F =

%e x - x^3 - 2*x^4 - 3*x^5 - 4*x^6 - 5*x^7 - 6*x^8 -...

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

%e x - 2*x^4 - 6*x^5 - 10*x^6 - 11*x^7 - 6*x^8 + 7*x^9 +...

%e (4) x+2*x^4 o x+1*x^3 o x-1*x^2 o 1*x o F =

%e x - 6*x^5 - 10*x^6 - 27*x^7 - 54*x^8 - 73*x^9 +...

%e (5) x+6*x^5 o x+2*x^4 o x+1*x^3 o x-1*x^2 o 1*x o F =

%e x - 10*x^6 - 27*x^7 - 54*x^8 - 253*x^9 +...

%o (PARI) {a(n)=local(F=x/(1-x+x*O(x^n)));if(n<1,0,if(n==1,1, for(k=2,n,c=-polcoeff(F,k);F=subst(x+c*x^k,x,F););return(c)))}

%Y Cf. A119460 (composition of x/(1-x)).

%K sign

%O 1,4

%A _Paul D. Hanna_, May 20 2006