A337808 O.g.f.: 1/(1 - x/(1 - 2^6*x/(1 - 3^6*x/(1 - 4^6*x/(1 - 5^6*x/(1 - 6^6*x/(1 -...))))))), a continued fraction.

1, 1, 65, 50881, 231455105, 4104215813761, 220579355255364545, 30221200809380332664641, 9302731197994837387680880385, 5843241203886533657008940262539521, 6942621504765123845961888310824174754625, 14676663615276526648053662674115841827580734401

Offset

0,3

Links

Table of n, a(n) for n=0..11.

Formula

a(n) ~ c * d^n * (n!)^6 / sqrt(n), where

d = 12^6 * Gamma(1/3)^6 / Gamma(1/6)^12 = 1.247526211138803516951432724912344768287048859917010218640563910368330569...

c = sqrt(3*d/Pi) = 1.091466801527496975151641909038030945303075901009696629477...

Mathematica

nmax = 15; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[Range[nmax + 1]^6*x]], {x, 0, nmax}], x]

Crossrefs

Cf. A001147, A000364, A216966, A227887, A337807, A337809.

Sequence in context: A269794 A242283 A061688 * A218689 A171706 A015072

Adjacent sequences: A337805 A337806 A337807 * A337809 A337810 A337811

Keyword

nonn

Author

Vaclav Kotesovec, Sep 23 2020

Status

approved