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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f. A(x) satisfies: A(x) = 1 + Sum_{n>=0} x^(2^n)*A(x)^(2^n)/(1 - x^(2^(n+1))).
EXAMPLE
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) +...
PROG
(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)}
CROSSREFS
Cf. A191768.
Sequence in context: A292216 A000669 A295461 * A221206 A281489 A225616
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 16 2011
STATUS
approved

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Last modified March 19 07:49 EDT 2024. Contains 370958 sequences. (Running on oeis4.)