A090004 Expansion of L(x)^(1/2), where L(x) is the g.f. for the Catalan Larcombe-French sequence A053175.

1, 4, 32, 320, 3616, 44160, 568320, 7587840, 104042496, 1455308800, 20671234048, 297204973568, 4315444576256, 63173752913920, 931171553771520, 13806071300751360, 205737584679321600, 3079516590086553600, 46275305227975393280, 697790255614687969280, 10554814464110079508480

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..833

Formula

a(n) = 2^n * A089603(n). - Seiichi Manyama, Jan 13 2019

a(n) ~ 2^(4*n - 1/2) / (n * sqrt(Pi*log(n))) * (1 - (gamma/2 + log(2))/log(n) + (3*gamma^2/8 + 3*log(2)*gamma/2 + 3*log(2)^2/2 - Pi^2/16) / log(n)^2), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Sep 29 2019

Mathematica

nmax = 25; CoefficientList[Series[(EllipticK[(8*x/(1 - 8*x))^2]/((1 - 8*x)*Pi/2))^(1/2), {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 26 2019 *)

Prog

(PARI) Vec( 1/agm(1, 1-16*x+O(x^66))^(1/2) ) \\ Joerg Arndt, Aug 14 2013

Crossrefs

Cf. A053175, A089602, A089603.

Sequence in context: A052704 A151403 A289427 * A357404 A371675 A061631

Adjacent sequences: A090001 A090002 A090003 * A090005 A090006 A090007

Keyword

nonn,easy

Author

Peter J Larcombe, Jan 19 2004

Extensions

More terms from Christian G. Bower, Jan 19 2004

Status

approved