A317855 - OEIS

%I #15 Jun 15 2021 11:10:04

%S 3,1,6,1,0,8,8,6,5,3,8,6,5,4,2,8,8,1,3,8,3,0,1,7,2,2,0,2,5,8,8,1,3,2,

%T 4,9,1,7,2,6,3,8,2,7,7,4,1,8,8,5,5,6,3,4,1,6,2,7,2,7,8,2,0,7,5,3,7,6,

%U 9,7,0,5,9,2,1,9,3,0,4,6,1,1,2,1,9,7,5,7,4,6,8,5,4,9,7,8,4,5,9,3,2,4,2,2,7

%N Decimal expansion of a constant related to the asymptotics of A122400.

%F Equals (1+exp(1/r))*r^2, where r = 0.873702433239668330496568304720719298213992... is the root of the equation exp(1/r)/r + (1+exp(1/r))*LambertW(-exp(-1/r)/r) = 0.

%e 3.161088653865428813830172202588132491726382774188556341627278...

%t r = r /. FindRoot[E^(1/r)/r + (1 + E^(1/r)) * ProductLog[-E^(-1/r)/r] == 0, {r, 3/4}, WorkingPrecision -> 120]; RealDigits[(1 + Exp[1/r])*r^2][[1]]

%o (PARI) r=solve(r=.8,1,exp(1/r)/r + (1+exp(1/r))*lambertw(-exp(-1/r)/r))

%o (1+exp(1/r))*r^2 \\ _Charles R Greathouse IV_, Jun 15 2021

%Y Cf. A121886, A122399, A122400, A122418, A122419, A122420, A227619, A232192, A243802, A244585, A248798, A317340, A326010.

%Y Cf. A301584, A301585, A301586, A303056, A303057.

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Aug 09 2018