A089156 a(n) = A069722(n+1)^2.

0, 16, 576, 25600, 1254400, 65028096, 3497066496, 192980975616, 10855179878400, 619683355033600, 35792910586740736, 2087229562810269696, 122682715414070296576, 7259332273021911040000, 432004345063916175360000, 25835779854133582469529600

Offset: 0

Author

Benoit Cloitre, Jan 03 2004

Keywords

• nonn

Crossrefs

Cf. A069722.

Programs

Mathematica

Flatten[{0, Table[2^(2*n) * Binomial[2*n, n]^2, {n, 1, 20}]}] (* Vaclav Kotesovec, Sep 28 2019 *)
CoefficientList[Series[-1 + 2*EllipticK[1 - 1/(1 - 64*x)] / (Pi*Sqrt[1 - 64*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 28 2019 *)

Formula

G.f.: 1/AGM(1, (1-64*x)^(1/2)).

E.g.f.: 1 + Sum[n>=0, a(n)*x^(2n)/(2n)! ] = BesselI(0, 4x)^2. - Ralf Stephan, Jan 11 2005

From Vaclav Kotesovec, Sep 28 2019: (Start)

For n > 0, a(n) = 2^(2*n) * binomial(2*n, n)^2.

a(n) ~ 2^(6*n) / (Pi*n). (End)