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

0,3

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