A171189 G.f. satisfies: AGM(1,A(x)) = 1/(1 - 4*x).

1, 8, 40, 176, 752, 3168, 13200, 54592, 224624, 920672, 3762240, 15337408, 62404656, 253505184, 1028426432, 4167385088, 16870487440, 68237238816, 275798010400, 1113973454464, 4496809953248, 18142920856576, 73165420555648

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Example

G.f.: A(x) = 1 + 8*x + 40*x^2 + 176*x^3 + 752*x^4 + 3168*x^5 +...
A(x)^(1/2) = 1 + 4*x + 12*x^2 + 40*x^3 + 144*x^4 + 528*x^5 + 1960*x^6 +...
(1+A(x))/2 = 1 + 4*x + 20*x^2 + 88*x^3 + 376*x^4 + 1584*x^5 + 6600*x^6 +...

Mathematica

CoefficientList[InverseSeries[Series[1/4 - EllipticK[1 - 1/x^2]/(2*Pi*x), {x, 1, 25}], x], x] (* Vaclav Kotesovec, Nov 15 2023 *)

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*4^n-2*polcoeff(agm(1, A), n))}

Crossrefs

Cf. A171188.

Sequence in context: A006726 A165665 A000760 * A272050 A270466 A270981

Adjacent sequences: A171186 A171187 A171188 * A171190 A171191 A171192

Keyword

nonn

Author

Paul D. Hanna, Dec 11 2009

Status

approved