A306770 - OEIS

%I #20 Feb 16 2025 08:33:55

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

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

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

%N Decimal expansion of Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!).

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>.

%F Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!) = exp(1) - 1 + gamma - ExpIntegralEi[1].

%F From _Amiram Eldar_, Jun 26 2021: (Start)

%F Equals Sum_{k>=2} 1/A054119(k).

%F Equals -Integral{x=0..1} x*log(x)*exp(x) dx. (End)

%e 0.40037967700464134050027...

%o (PARI) exp(1) - 1 + Euler - real(-eint1(-1)) \\ _Michel Marcus_, Mar 09 2019

%Y Cf. A001113 (exp(1)), A001620 (gamma), A054119, A091725 (ExpIntegralEi[1]).

%K nonn,cons,changed

%O 0,1

%A _Seiichi Manyama_, Mar 09 2019