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 A058299 #17 Aug 29 2018 06:31:31
%S A058299 1,2,4,5,10,15,20,16,38,30,67,49,63,80,92,139,173,99,127,159,190,198,
%T A058299 423,198,259,221,326,631,394,273,280,341,359,397,539,418,518,533,662,
%U A058299 3502,735,815,701,706,611,839,793,768,781,983,858,1035,883,3476,1154
%N A058299 Sum of terms in simple continued fraction for Sum_{k=0..n} 1/k!.
%H A058299 Robert Israel, <a href="/A058299/b058299.txt">Table of n, a(n) for n = 0..3300</a>
%e A058299 a(3) = 2 + 1 + 2 = 5 because 1/0! + 1/1! + 1/2! + 1/3! = 8/3 = 2 + 1/(1 + 1/2).
%p A058299 seq(convert(numtheory:-cfrac(add(1/k!,k=0..n),quotients),`+`), n=0..100); # _Robert Israel_, Aug 29 2018
%o A058299 (PARI) a(n) = vecsum(contfrac(sum(k=0, n, 1/k!))); \\ _Michel Marcus_, Aug 29 2018
%Y A058299 Cf. A069880 (number of summands).
%K A058299 easy,nonn,look
%O A058299 0,2
%A A058299 _Leroy Quet_, Dec 07 2000