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A089602 Expansion of L(x)^(1/4), where L(x) = o.g.f. for A053175. 6
1, 2, 14, 132, 1446, 17340, 220524, 2919240, 39761094, 553080044, 7818246436, 111929301688, 1618972088028, 23616939932376, 346986771074328, 5129262870441360, 76223971339368006, 1137977844577647948, 17058656523389665268, 256642078290095158360, 3873624648355421605492 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A146971 A246481 A048990 * A336960 A052641 A157085
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Dec 30 2003
STATUS
approved

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Last modified April 16 19:05 EDT 2024. Contains 371751 sequences. (Running on oeis4.)