A158100 G.f. satisfies: A(x) = 1/AGM(1, 1 - 8*x/A(x) ).

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

Offset: 0

Author

Paul D. Hanna, Mar 13 2009

Keywords

• sign

Comments

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

Examples

			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)
		

Crossrefs

Cf. A060691, A158101 (bisection), A258053.

Cf. A158122 (sqrt), A158212, A158213.

Programs

PARI

{a(n)=polcoeff(x/serreverse(x/agm(1,1-8*x +x*O(x^n))),n)}

Formula

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

Convolution square-root 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