A193203 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, 8, 136, 8256, 1405440, 602922752, 618218766848, 1468496379454976, 7913439173996188672, 95288304033198904688640, 2534320562857451371729985536, 147510069367873486819642346127360, 18647939279377935249755798151259226112

Offset

1,2

Links

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

Example

 G.f.: A(x) = x + 2*x^2 + 8*x^3 + 136*x^4 + 8256*x^5 + 1405440*x^6 +...
where
A(A(x)) = x*(1+2*x) + 2*x^2*(1+4*x)^2 + 8*x^3*(1+8*x)^3 + 136*x^4*(1+16*x)^4 + 8256*x^5*(1+32*x)^5 +...+ a(n)*x^n*(1+2^n*x)^n +...
Explicitly,
A(A(x)) = x + 4*x^2 + 24*x^3 + 360*x^4 + 18496*x^5 + 2939392*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. A193204.

Sequence in context: A337296 A111827 A045330 * A259126 A140050 A318038

Adjacent sequences: A193200 A193201 A193202 * A193204 A193205 A193206

Keyword

nonn

Author

Paul D. Hanna, Jul 19 2011

Status

approved