OFFSET
1,6
EXAMPLE
The iterated iterations of g.f. A(x) begin:
A(x) = (1)x + x^2 - x^3 + x^4 + x^5 - 11x^6 + 23x^7 - 20x^8 + 731x^9+..
A(A(x)) = x + (2)x^2 - 2x^4 + 6x^5 - 8x^6 - 50x^7 + 78x^8 + 1688x^9+...
A(A(A(x))) = x + 3x^2 + (3)x^3 - 3x^4 - x^5 + 17x^6 - 81x^7 -370x^8+...
A(A(A(A(x)))) = x + 4x^2 + 8x^3 + (4)x^4 - 12x^5 + 4x^6 + 12x^7 +...
A(A(A(A(A(x))))) = x + 5x^2 + 15x^3 + 25x^4 + (5)x^5 - 55x^6 -33x^7+...
A(A(A(A(A(A(x)))))) = x + 6x^2 + 24x^3 + 66x^4 + 106x^5 + (4)x^6 +...
Coefficients [x^n] of n-th self-composition of A(x) forms A119816:
[1,2,3,4,5,4,7,8,3,9,11,4,13,11,14,8,17,4,19,4,1,4,23,24,5,17,27,...].
PROG
(PARI) {a(n)=local(F=x+x^2+sum(k=3, n-1, a(k)*x^k), G=x+x*O(x^n)); if(n<1, 0, if(n<=2, 1, for(k=1, n, G=subst(F, x, G)); return((n-polcoeff(G, n, x)) )))}
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 31 2006
STATUS
approved