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A090004
Expansion of L(x)^(1/2), where L(x) is the g.f. for the Catalan Larcombe-French sequence A053175.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Peter J Larcombe, Jan 19 2004
EXTENSIONS
More terms from Christian G. Bower, Jan 19 2004
STATUS
approved