%I #50 Feb 06 2019 02:27:14

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

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

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

%N Decimal expansion of Sum_{n>=1} log(n+1)/n!.

%C Equal to log(2*exp(1/2*log(3*exp(1/3*log(4*exp(...)))))). - _Rok Cestnik_, Jan 31 2019

%e 1.55867043642538904...

%t NSum[ Log[n + 1]/n!, {n, 1, Infinity}, WorkingPrecision -> 110, NSumTerms -> 100] // RealDigits[#, 10, 105]& // First (* _Jean-François Alcover_, Feb 20 2013 *)

%o (PARI) suminf(n=1, log(n+1)/n!) \\ _Michel Marcus_, Jan 31 2019

%Y Cf. A306243.

%K nonn,cons

%O 1,2

%A _N. J. A. Sloane_, Aug 23 2011, based on a posting by Richard C. Schroeppel to the Math Fun Mailing List

%E More terms from _Alois P. Heinz_, Aug 28 2011