A191768 G.f. a(x) satisfies: A(x) = 1 + Sum_{n>=1} x^n*A(x)^A000265(n) where A000265(n) = largest odd divisor of n.

1, 1, 2, 4, 10, 25, 68, 193, 565, 1688, 5136, 15854, 49517, 156191, 496836, 1591924, 5133091, 16643856, 54234349, 177505376, 583272256, 1923482331, 6363842492, 21117432227, 70265970878, 234388421515, 783664894313, 2625748635300

Offset: 0

Author

Paul D. Hanna, Jun 16 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 25*x^5 + 68*x^6 + 193*x^7 +...
The g.f. satisfies the following identities:
A(x) = 1 + x*A(x) + x^2*A(x) + x^3*A(x)^3 + x^4*A(x) + x^5*A(x)^5 + x^6*A(x)^3 + x^7*A(x)^7 + x^8*A(x) +...+ x^n*A(x)^A000265(n) +...
A(x) = 1 + x*A(x)/(1-x^2*A(x)^2) + x^2*A(x)/(1-x^4*A(x)^2) + x^4*A(x)/(1-x^8*A(x)^2) + x^8*A(x)/(1-x^16*A(x)^2) +...
		

Crossrefs

Cf. A191769.

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))^(m/2^valuation(m,2))));polcoeff(A,n)}

Formula

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