A337807 O.g.f.: 1/(1 - x/(1 - 2^5*x/(1 - 3^5*x/(1 - 4^5*x/(1 - 5^5*x/(1 - 6^5*x/(1 -...))))))), a continued fraction.

1, 1, 33, 8865, 10401345, 38103228225, 352780110115425, 7139708074971014625, 284135772494258636522625, 20513418606891012201924650625, 2521576999908767233729260158270625, 501403316300941434382591838239147790625, 154613553816538472779474765739707728587090625

Offset

0,3

Links

Table of n, a(n) for n=0..12.

Formula

a(n) ~ c * d^n * (n!)^5 / sqrt(n), where

d = 10^5 * Gamma(2/5)^5 / Gamma(1/5)^10 = 1.29133469292029895399895579276779248119508048136258551947012306768...

c = sqrt(5*d/(2*Pi)) = 1.0137117429632556021458475899461841562723826775113969124...

Mathematica

nmax = 15; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[Range[nmax + 1]^5*x]], {x, 0, nmax}], x]

Crossrefs

Cf. A001147, A000364, A216966, A227887, A337808, A337809.

Sequence in context: A060705 A061687 A116056 * A232148 A229845 A232306

Adjacent sequences: A337804 A337805 A337806 * A337808 A337809 A337810

Keyword

nonn

Author

Vaclav Kotesovec, Sep 23 2020

Status

approved