OFFSET
0,2
COMMENTS
See A060691 for the expansion of AGM(1,1-8x), where AGM denotes the arithmetic-geometric mean.
LINKS
Otto Dirk, Störungstheorie des Anderson-Modells: Untersuchung und Erweiterung der NCA und DMFT, Dr. rer. nat. thesis, Universität Dortmund, 2003 [in German]. It appears that the table on p. 48 contains this sequence.
FORMULA
A bisection of A158100.
G.f. satisfies: A(x^2) = -4*x + x/Series_Reversion( x/AGM(1,1-8*x) ).
From Paul D. Hanna, Feb 04 2010: (Start)
G.f. satisfies: A(x) = Sum_{n>=0} C(2n,n)^2*x^n/A(x)^(2n).
G.f.: A(x) = [x/Series_Reversion(x*G(x)^2)]^(1/2) where G(x) = Sum_{n>=0} C(2n,n)^2*x^n = 1/AGM(1, (1-16*x)^(1/2)) = g.f. of A002894.
(End)
EXAMPLE
G.f.: A(x) = 1 + 4*x + 4*x^2 - 16*x^3 - 28*x^4 + 176*x^5 + 336*x^6 - ...
PROG
(PARI) {a(n)=polcoeff(-4*x+x/serreverse(x/agm(1, 1-8*x +O(x^(2*n+1)))), 2*n)}
(PARI) {a(n)=local(G=sum(m=0, n, binomial(2*m, m)^2*x^m)+x*O(x^n)); polcoeff((x/serreverse(x*G^2))^(1/2), n)} \\ Paul D. Hanna, Feb 04 2010
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Mar 13 2009
STATUS
approved