

A158100


G.f. satisfies: A(x) = 1/AGM(1, 1  8*x/A(x) ).


6



1, 4, 4, 0, 4, 0, 16, 0, 28, 0, 176, 0, 336, 0, 2496, 0, 4956, 0, 40112, 0, 81488, 0, 694720, 0, 1432688, 0, 12647488, 0, 26360896, 0, 238598400, 0, 501256668, 0, 4623092400, 0, 9772018896, 0, 91458048960, 0, 194263943664, 0, 1839634167360
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OFFSET

0,2


COMMENTS

See A060691 for the expansion of AGM(1,18x), where AGM denotes the arithmeticgeometric mean.


LINKS

Table of n, a(n) for n=0..42.


FORMULA

G.f.: A(x) = x/Series_Reversion( x/AGM(1, 18*x) ).
Convolution squareroot is A158122, which has two nonzero quadrisections, A158212 and A158213, that are inverse convolutions of each other (by a factor of 2).  Paul D. Hanna, Mar 14 2009


EXAMPLE

G.f.: A(x) = 1 + 4*x + 4*x^2 + 4*x^4  16*x^6  28*x^8 +...
1  8*x/A(x) = 1  8*x + 32*x^2  96*x^3 + 256*x^4  608*x^5 +...
From Paul D. Hanna, Mar 14 2009: (Start)
Convolution square root is A158122 and begins:
[1,2,0,0,2,4,0,0,16,40,0,0,200,544,0,0,3006,8540,0,0,...]
in which the convolution of the quadrisections equals 2:
[1,2,16,200,3006,...]*[2,4,40,544,8540,...] = 2. (End)


PROG

(PARI) {a(n)=polcoeff(x/serreverse(x/agm(1, 18*x +x*O(x^n))), n)}


CROSSREFS

Cf. A060691, A158101 (bisection), A258053.
Cf. A158122 (sqrt), A158212, A158213.
Sequence in context: A187149 A106508 A177036 * A104287 A174611 A283361
Adjacent sequences: A158097 A158098 A158099 * A158101 A158102 A158103


KEYWORD

sign


AUTHOR

Paul D. Hanna, Mar 13 2009


STATUS

approved



