OFFSET
1,3
EXAMPLE
G.f.: A(x) = x + x^2 + 2*x^3 + 11*x^4 + 142*x^5 + 3394*x^6 +...
where
A(A(x)) = x*(1+x) + x^2*(1+2*x)^2 + 2*x^3*(1+3*x)^3 + 11*x^4*(1+4*x)^4 + 142*x^5*(1+5*x)^5 + 3394*x^6*(1+6*x)^6 +...+ a(n)*x^n*(1+n*x)^n +...
Explicitly,
A(A(x)) = x + 2*x^2 + 6*x^3 + 33*x^4 + 372*x^5 + 8054*x^6 + 288868*x^7 +...
PROG
(PARI) {a(n)=local(A=[1], F=x, G=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A);
G=sum(m=1, #A-1, A[m]*x^m*(1+m*x +x*O(x^#A))^m );
A[#A]=Vec(G)[#A]-Vec(subst(F, x, F))[#A]); if(n<1, 0, A[n])}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 19 2011
STATUS
approved