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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

Table of n, a(n) for n=0..27.

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

Adjacent sequences:  A191766 A191767 A191768 * A191770 A191771 A191772

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 16 2011

STATUS

approved

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Last modified November 27 07:28 EST 2021. Contains 349365 sequences. (Running on oeis4.)