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A158101 G.f. satisfies: A(x^2) = -4*x + 1/AGM(1, 1 - 8*x/(A(x^2) + 4*x) ). 2
1, 4, 4, -16, -28, 176, 336, -2496, -4956, 40112, 81488, -694720, -1432688, 12647488, 26360896, -238598400, -501256668, 4623092400, 9772018896, -91458048960, -194263943664, 1839634167360, 3923099632704, -37510172125440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See A060691 for the expansion of AGM(1,1-8x), where AGM denotes the arithmetic-geometric mean.

LINKS

Table of n, a(n) for n=0..23.

FORMULA

A bisection of A158100.

G.f. satisfies: A(x^2) = -4*x + x/Series_Reversion( x/AGM(1,1-8*x) ).

Contribution 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)} [From Paul D. Hanna, Feb 04 2010]

CROSSREFS

Cf. A060691, A158100.

Cf. A002894. [From Paul D. Hanna, Feb 04 2010]

Sequence in context: A065732 A092959 A183433 * A038234 A099462 A218051

Adjacent sequences:  A158098 A158099 A158100 * A158102 A158103 A158104

KEYWORD

sign

AUTHOR

Paul D. Hanna, Mar 13 2009

STATUS

approved

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Last modified June 27 11:25 EDT 2017. Contains 288788 sequences.