A191769 G.f. A(x) satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^A006519(n) where A006519(n) = highest power of 2 dividing n.

1, 1, 2, 5, 12, 33, 92, 267, 792, 2403, 7414, 23199, 73454, 234901, 757654, 2461877, 8051284, 26480681, 87534184, 290652931, 968992200, 3242229475, 10884245838, 36648566551, 123739675390, 418848744517, 1421072269234, 4831811596381

Offset: 0

Author

Paul D. Hanna, Jun 16 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 12*x^4 + 33*x^5 + 92*x^6 + 267*x^7 +...
The g.f. satisfies the following relations:
A(x) = 1 + x*A(x) + x^2*A(x)^2 + x^3*A(x) + x^4*A(x)^4 + x^5*A(x) + x^6*A(x)^2 + x^7*A(x) + x^8*A(x)^8 +...+ x^n*A(x)^A006519(n) +...
A(x) = 1 + x*A(x)/(1-x^2) + x^2*A(x)^2/(1-x^4) + x^4*A(x)^4/(1-x^8) + x^8*A(x)^8/(1-x^16) + x^16*A(x)^16/(1-x^32) +...
		

Crossrefs

Cf. A191768.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(2^valuation(m,2))));polcoeff(A,n)}

Formula

G.f. A(x) satisfies: A(x) = 1 + Sum_{n>=0} x^(2^n)*A(x)^(2^n)/(1 - x^(2^(n+1))).