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
Keywords
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
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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))).