A158213 A quadrisection of A158122: a(n) = A158122(4n+1).

2, -4, 40, -544, 8540, -145720, 2625648, -49161024, 947069352, -18650752400, 373773754912, -7598155324032, 156294309718944, -3247203559571136, 68042170392274560, -1436308791802028544, 30514944039812500572

Offset

0,1

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..16.

Formula

G.f.: A(x) = 2/B(x) where B(x) is the g.f. of A158212;

let F(x) = 2/A(x^4) + x*A(x^4) be the g.f. of A158122

then F(x) satisfies: F(x)^2 = 1/AGM(1, 1 - 8*x/F(x)^2 ).

Example

G.f.: A(x) = 2 - 4*x + 40*x^2 - 544*x^3 + 8540*x^4 - 145720*x^5 +...
2/A(x) = 1 + 2*x - 16*x^2 + 200*x^3 - 3006*x^4 + 49956*x^5 +...
F(x) = 1 + 2*x + 2*x^4 - 4*x^5 - 16*x^8 + 40*x^9 + 200*x^12 - 544*x^13 +...
where F(x) = 2/A(x^4) + x*A(x^4) is the g.f. of A158122.

Prog

(PARI) {a(n)=polcoeff(sqrt(x/serreverse(x/agm(1, 1-8*x +O(x^(4*n+2))))), 4*n+1)}

Crossrefs

Cf. A158122, A158212, A158100, A060691.

Sequence in context: A326483 A187468 A238719 * A012596 A292700 A012676

Adjacent sequences: A158210 A158211 A158212 * A158214 A158215 A158216

Keyword

sign

Author

Paul D. Hanna, Mar 14 2009

Status

approved