This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A306770 #20 Feb 16 2025 08:33:55
%S A306770 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 A306770 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 A306770 0,5,2,2,5,9,7,4,0,8,1,1,1,9,5,9,4,2,8,5,3,1
%N A306770 Decimal expansion of Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!).
%H A306770 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ExponentialIntegral.html">Exponential Integral</a>.
%F A306770 Sum_{k>=0} 1/(k! + (k+1)! + (k+2)!) = exp(1) - 1 + gamma - ExpIntegralEi[1].
%F A306770 From _Amiram Eldar_, Jun 26 2021: (Start)
%F A306770 Equals Sum_{k>=2} 1/A054119(k).
%F A306770 Equals -Integral{x=0..1} x*log(x)*exp(x) dx. (End)
%e A306770 0.40037967700464134050027...
%o A306770 (PARI) exp(1) - 1 + Euler - real(-eint1(-1)) \\ _Michel Marcus_, Mar 09 2019
%Y A306770 Cf. A001113 (exp(1)), A001620 (gamma), A054119, A091725 (ExpIntegralEi[1]).
%K A306770 nonn,cons
%O A306770 0,1
%A A306770 _Seiichi Manyama_, Mar 09 2019