A193192 G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n * (1+x)^(n^2), where g.f. A(x) = Sum_{n>=1} a(n)*x^n.

1, 1, 2, 13, 184, 4725, 188596, 10765407, 829780846, 82924007284, 10420182259194, 1607406366386249, 298555458341808338, 65711158773953092780, 16910051487116790543954, 5030141451818448773854244, 1712632076858599057432066794

Offset: 1

Author

Paul D. Hanna, Jul 19 2011

Keywords

• nonn

Examples

			G.f.: A(x) = x + x^2 + 2*x^3 + 13*x^4 + 184*x^5 + 4725*x^6 +...
where
A(A(x)) = x*(1+x) + x^2*(1+x)^4 + 2*x^3*(1+x)^9 + 13*x^4*(1+x)^16 + 184*x^5*(1+x)^25 + 4725*x^6*(1+x)^36 +...+ a(n)*x^n*(1+x)^(n^2) +...
Explicitly,
A(A(x)) = x + 2*x^2 + 6*x^3 + 37*x^4 + 468*x^5 + 11054*x^6 + 421428*x^7 +...
		

Crossrefs

Cf. A193193, A193194, A193195.

Programs

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^2));
A[#A]=Vec(G)[#A]-Vec(subst(F,x,F))[#A]);if(n<1,0,A[n])}