OFFSET
1,4
EXAMPLE
G.f.: A(x) = x + x^2 + x^3 + 3*x^4 + 20*x^5 + 262*x^6 + 5367*x^7 +...
where
A(A(x)) = x*(1+x) + x^2*(1+x)^3 + x^3*(1+x)^6 + 3*x^4*(1+x)^10 + 20*x^5*(1+x)^15 + 262*x^6*(1+x)^21 +...+ a(n)*x^n*(1+x)^(n*(n+1)/2) +...
Explicitly,
A(A(x)) = x + 2*x^2 + 4*x^3 + 12*x^4 + 66*x^5 + 717*x^6 + 13344*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+x+x*O(x^#A))^(m*(m+1)/2));
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