A245928 G.f. satisfies: A(x) = 1 + x*AGM(A(x)^4, A(-x)^4).

1, 1, 0, 2, 0, 5, 0, 12, 0, 20, 0, -30, 0, -546, 0, -3672, 0, -18796, 0, -79640, 0, -270955, 0, -584340, 0, 903396, 0, 20471948, 0, 155046180, 0, 872787888, 0, 4012121412, 0, 14728928136, 0, 34982326212, 0, -40695186320, 0, -1194336566976, 0, -9612277504606, 0, -56604770338290, 0

Offset

0,4

Comments

Here AGM(x,y) = AGM((x+y)/2, sqrt(x*y)) denotes the arithmetic-geometric mean.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..350

Formula

G.f. satisfies: A(x) = 1 + x*AGM( (A(x)^4 + A(-x)^4)/2, A(x)^2*A(-x)^2 ).

Example

G.f.: A(x) = 1 + x + 2*x^3 + 5*x^5 + 12*x^7 + 20*x^9 - 30*x^11 - 546*x^13 -...
where
AGM(A(x)^4,A(-x)^4) = 1 + 2*x^2 + 5*x^4 + 12*x^6 + 20*x^8 - 30*x^10 - 546*x^12 -...
RELATED SERIES:
A(x)^2 = 1 + 2*x + x^2 + 4*x^3 + 4*x^4 + 10*x^5 + 14*x^6 + 24*x^7 + 44*x^8 +...
A(x)^4 = 1 + 4*x + 6*x^2 + 12*x^3 + 25*x^4 + 44*x^5 + 92*x^6 + 156*x^7 + 308*x^8 +...
(A(x)^4 + A(-x)^4)/2 = 1 + 6*x^2 + 25*x^4 + 92*x^6 + 308*x^8 + 878*x^10 + 1614*x^12 -...
A(x)^2*A(-x)^2 = 1 - 2*x^2 - 7*x^4 - 20*x^6 - 44*x^8 - 26*x^10 + 494*x^12 + 4152*x^14 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1 + x*agm(A^4, subst(A, x, -x +x*O(x^n))^4)); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Sequence in context: A242682 A281731 A361921 * A242839 A105523 A210628

Adjacent sequences: A245925 A245926 A245927 * A245929 A245930 A245931

Keyword

sign

Author

Paul D. Hanna, Aug 15 2014

Status

approved