login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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, 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 (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)/(1 - x^(2*2^n)*A(x)^2).

EXAMPLE

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) +...

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

CROSSREFS

Cf. A191769.

Sequence in context: A124501 A124344 A049125 * A027432 A032128 A052829

Adjacent sequences:  A191765 A191766 A191767 * A191769 A191770 A191771

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 16 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 15:02 EDT 2019. Contains 321330 sequences. (Running on oeis4.)