

A214761


G.f. satisfies: A(x) = 1/A(x*A(x)).


8



1, 2, 4, 12, 40, 128, 416, 1344, 4224, 12928, 38016, 104832, 260096, 512256, 329728, 4140032, 33444864, 184423424, 883798016, 3935711232, 16759001088, 69266997248, 280327684096, 1116872122368, 4394989174784, 17112512544768, 65974620848128
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OFFSET

0,2


COMMENTS

Compare g.f. to: G(x) = 1/G(x*G(x)) when G(x) = 1/(1x).
An infinite number of functions G(x) satisfy (*) G(x) = 1/G(x*G(x)); for example, (*) is satisfied by G(x) = 1/(1m*x).


LINKS

Table of n, a(n) for n=0..26.


FORMULA

The g.f. of this sequence is the limit of the recurrence:
(*) G_{n+1}(x) = (G_n(x) + 1/G_n(x*G_n(x)))/2 starting at G_0(x) = 1+2*x.


EXAMPLE

G.f.: A(x) = 1 + 2*x + 4*x^2 + 12*x^3 + 40*x^4 + 128*x^5 + 416*x^6 + 1344*x^7 +...
Related expansions:
1/A(x) = A(x*A(x)) = 1  2*x  4*x^3  8*x^4  16*x^5  48*x^6  96*x^7  128*x^8 + 64*x^9 + 2048*x^10 +...


PROG

(PARI) {a(n)=local(A=1+2*x); for(i=0, n, A=(A+1/subst(A, x, x*A^1+x*O(x^n)))/2); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))


CROSSREFS

Cf. A214762, A214763, A214764, A214765, A214766, A214767, A214768, A214769.
Sequence in context: A099214 A126946 A113179 * A327845 A056236 A300652
Adjacent sequences: A214758 A214759 A214760 * A214762 A214763 A214764


KEYWORD

sign


AUTHOR

Paul D. Hanna, Jul 29 2012


STATUS

approved



