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 A353545 #17 May 28 2022 02:11:12
%S A353545 1,5,47,379,9487,14233,87179,44635753,1205165611,6025828181,
%T A353545 729125211161,972166948343,54765404757169,71879593743829,
%U A353545 25876653747779441,6624423359431551911,1914458350875718742519,51690375473644406388353,18660225545985630712321553,186602255459856307126125437
%N A353545 a(n) is the numerator of Sum_{k=1..n} 1 / (k*k!).
%F A353545 Numerators of coefficients in expansion of (Ei(x) - log(x) - gamma) / (1 - x), x > 0.
%e A353545 1, 5/4, 47/36, 379/288, 9487/7200, 14233/10800, 87179/66150, ...
%t A353545 Table[Sum[1/(k k!), {k, 1, n}], {n, 1, 20}] // Numerator
%t A353545 nmax = 20; Assuming[x > 0, CoefficientList[Series[(ExpIntegralEi[x] - Log[x] - EulerGamma)/(1 - x), {x, 0, nmax}], x]] // Numerator // Rest
%o A353545 (PARI) a(n) = numerator(sum(k=1, n, 1/(k*k!))); \\ _Michel Marcus_, May 26 2022
%o A353545 (Python)
%o A353545 from math import factorial
%o A353545 from fractions import Fraction
%o A353545 def A353545(n): return sum(Fraction(1, k*factorial(k)) for k in range(1,n+1)).numerator # _Chai Wah Wu_, May 27 2022
%Y A353545 Cf. A001563, A053557, A061354, A103816, A120265, A229837, A354401 (denominators), A354402.
%K A353545 nonn,frac
%O A353545 1,2
%A A353545 _Ilya Gutkovskiy_, May 25 2022