A193204 G.f. satisfies: A(A(x)) = Sum_{n>=1} a(n)*x^n / (1-2^n*x)^n, where g.f. A(x) = Sum_{n>=1} a(n)*x^n.

1, 2, 12, 264, 18192, 3363168, 1536410944, 1659081681024, 4119831378999040, 23085227981131301376, 287864665471943041639424, 7902500071635377252245854208, 473485024165978066993819500335104, 61476984240894226792319001395455369216

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Example

 G.f.: A(x) = x + 2*x^2 + 12*x^3 + 264*x^4 + 18192*x^5 + 3363168*x^6 +...
where
A(A(x)) = x/(1-2*x) + 2*x^2/(1-4*x)^2 + 12*x^3/(1-8*x)^3 + 264*x^4/(1-16*x)^4 + 18192*x^5/(1-32*x)^5 +...+ a(n)*x^n/(1-2^n*x)^n +...
Explicitly,
A(A(x)) = x + 4*x^2 + 32*x^3 + 656*x^4 + 40224*x^5 + 7013760*x^6 +...

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/(1-2^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

Cf. A193203.

Sequence in context: A012549 A009610 A012546 * A289314 A091504 A098137

Adjacent sequences: A193201 A193202 A193203 * A193205 A193206 A193207

Keyword

nonn

Author

Paul D. Hanna, Jul 19 2011

Status

approved