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%I #18 Sep 29 2019 08:47:34
%S 1,2,14,132,1446,17340,220524,2919240,39761094,553080044,7818246436,
%T 111929301688,1618972088028,23616939932376,346986771074328,
%U 5129262870441360,76223971339368006,1137977844577647948,17058656523389665268,256642078290095158360,3873624648355421605492
%N Expansion of L(x)^(1/4), where L(x) = o.g.f. for A053175.
%H Seiichi Manyama, <a href="/A089602/b089602.txt">Table of n, a(n) for n = 0..834</a>
%F G.f.: (2*EllipticK(8*x/(1-8*x))/((1-8*x)*Pi))^(1/4).
%F a(n) ~ 2^(4*n - 7/4) / (Pi^(1/4) * n * log(n)^(3/4)) * (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
%t nmax = 25; CoefficientList[Series[(EllipticK[(8*x/(1 - 8*x))^2]/((1 - 8*x)*Pi/2))^(1/4), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 26 2019 *)
%o (PARI) Vec(1/agm(1,1-16*x+O(x^66))^(1/4)) \\ _Joerg Arndt_, Aug 14 2013
%Y Cf. A053175, A090004.
%K nonn
%O 0,2
%A _Vladeta Jovovic_, Dec 30 2003
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