A089602 Expansion of L(x)^(1/4), where L(x) = o.g.f. for A053175.

1, 2, 14, 132, 1446, 17340, 220524, 2919240, 39761094, 553080044, 7818246436, 111929301688, 1618972088028, 23616939932376, 346986771074328, 5129262870441360, 76223971339368006, 1137977844577647948, 17058656523389665268, 256642078290095158360, 3873624648355421605492

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..834

Formula

G.f.: (2*EllipticK(8*x/(1-8*x))/((1-8*x)*Pi))^(1/4).

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

Mathematica

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 *)

Prog

(PARI) Vec(1/agm(1, 1-16*x+O(x^66))^(1/4)) \\ Joerg Arndt, Aug 14 2013

Crossrefs

Cf. A053175, A090004.

Sequence in context: A146971 A246481 A048990 * A336960 A052641 A157085

Adjacent sequences: A089599 A089600 A089601 * A089603 A089604 A089605

Keyword

nonn

Author

Vladeta Jovovic, Dec 30 2003

Status

approved