A171188 G.f. satisfies: AGM(1,A(x)) = 1 + 4*x.

1, 8, 8, -16, 48, -160, 528, -1600, 3952, -4512, -31040, 322496, -2021584, 10452384, -47768512, 196396032, -719709808, 2244001312, -5014625888, -511332480, 96425281504, -773680460288, 4504107424128, -22283547559808, 97629901795824

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Example

G.f.: A(x) = 1 + 8*x + 8*x^2 - 16*x^3 + 48*x^4 - 160*x^5 + 528*x^6 +...
A(x)^(1/2) = 1 + 4*x - 4*x^2 + 8*x^3 - 16*x^4 + 16*x^5 + 104*x^6 +...
(1+A(x))/2 = 1 + 4*x + 4*x^2 - 8*x^3 + 24*x^4 - 80*x^5 + 264*x^6 +...

Prog

(PARI) {a(n)=local(A=1+8*x+sum(m=2, n-1, a(m)*x^m)+x^2*O(x^n)); if(n<2, polcoeff(A, n), -2*polcoeff(agm(1, A), n))}

Crossrefs

Cf. A171189.

Sequence in context: A309461 A245420 A022091 * A145909 A168409 A135405

Adjacent sequences: A171185 A171186 A171187 * A171189 A171190 A171191

Keyword

sign

Author

Paul D. Hanna, Dec 11 2009

Status

approved