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A174846 E.g.f.: AGM(1, exp(4x)), where AGM(x, y) is the arithmetic-geometric mean of Gauss. 0
1, 2, 6, 20, 66, 212, 756, 3320, 11346, -11068, 14556, 7202120, 18928476, -1376971048, -3526491144, 394396083920, 1016723438706, -148493230507228, -383613651929844, 71479338751223720, 184867683069498036 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Conjecture: limit |a(n)/n!|^(-1/n) = r exists and is finite with r<0.8...

What is the radius of convergence of the e.g.f. as a power series in x?

LINKS

Table of n, a(n) for n=0..20.

FORMULA

E.g.f.: exp(2x)*AGM(1, cosh(2x)).

E.g.f.: exp(2x)*AGM( cosh(x)^2, sqrt(cosh(2x)) ).

EXAMPLE

E.g.f.: A(x) = 1 + 2*x + 6*x^2/2! + 20*x^3/3! + 66*x^4/4! +...

Special value:

A(log(2)/8) = Pi^(3/2)*sqrt(8)/gamma(1/4)^2 = 1.19814023473...

PROG

(PARI) {a(n)=n!*polcoeff(agm(1, exp(4*x+x*O(x^n))), n)}

CROSSREFS

Sequence in context: A027061 A279460 A083323 * A111285 A052991 A246019

Adjacent sequences:  A174843 A174844 A174845 * A174847 A174848 A174849

KEYWORD

sign

AUTHOR

Paul D. Hanna, Jan 24 2011

STATUS

approved

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Last modified April 18 16:38 EDT 2019. Contains 322209 sequences. (Running on oeis4.)