A119460 Composition of function F = x/(1-x) from functions of the form [x + a(n)*x^n]: F = a(1)*x o x+a(2)*x^2 o x+a(3)*x^3 o ... o x+a(n)*x^n o ...

1, 1, 1, -1, 3, -3, 6, -15, 58, -64, 198, -476, 1179, -2907, 8377, -19917, 69243, -131621, 379716, -995100, 2878526, -7230486, 21469716, -54741166, 156719748, -417925683, 1220839292, -3221204589, 9501389898, -25010664810, 73038583431, -197176327311, 595340630241

Offset

1,5

Links

Table of n, a(n) for n=1..33.

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

Cf. A119459 (decomposition of x/(1-x)).

Sequence in context: A345908 A006807 A298180 * A348539 A095356 A123104

Adjacent sequences: A119457 A119458 A119459 * A119461 A119462 A119463

Keyword

sign

Author

Paul D. Hanna, May 20 2006

Status

approved