OFFSET
1,3
COMMENTS
A(A(A(A(A(A(x)))))) is the 6th self-composition of the g.f. A(x).
EXAMPLE
G.f.: A(x) = x + x^2 + 30*x^3 + 2385*x^4 + 273560*x^5 +...
A(A(x)) = x + 2*x^2 + 62*x^3 + 4921*x^4 + 564280*x^5 +...
A(A(A(x))) = x + 3*x^2 + 96*x^3 + 7614*x^4 + 872950*x^5 +...
A(A(A(A(x)))) = x + 4*x^2 + 132*x^3 + 10470*x^4 + 1200384*x^5 +...
A(A(A(A(A(x))))) = x + 5*x^2 + 170*x^3 + 13495*x^4 + 1547420*x^5 +...
A(A(A(A(A(A(x)))))) = x + 6*x^2 + 210*x^3 + 16695*x^4 + 1914920*x^5 +...
so that 7*A(x) = A(A(A(A(A(A(x)))))) + 6*x + x^2.
PROG
(PARI) {a(n)=local(A=x+x^2, G); if(n<1, 0, for(i=3, n+1, G=x; for(j=1, 6, G=subst(A, x, G+x*O(x^i))); A=A+polcoeff(G, i)*x^i); polcoeff(A, n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 03 2008
STATUS
approved