login
A158213
A quadrisection of A158122: a(n) = A158122(4n+1).
3
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.
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
KEYWORD
sign
AUTHOR
Paul D. Hanna, Mar 14 2009
STATUS
approved