A337807 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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