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 A354402 #15 May 27 2022 21:14:23
%S A354402 1,3,29,229,5737,8603,210781,26979863,728456581,3642282779,
%T A354402 440716217519,1762864869691,297924162982399,260683642609331,
%U A354402 15641018556560861,4004100750479565401,1157185116888594641129,31243998155992054970143,11279083334313131850347743,112790833343131318500567523
%N A354402 a(n) is the numerator of Sum_{k=1..n} (-1)^(k+1) / (k*k!).
%F A354402 Numerators of coefficients in expansion of (gamma + log(x) - Ei(-x)) / (1 - x), x > 0.
%e A354402 1, 3/4, 29/36, 229/288, 5737/7200, 8603/10800, 210781/264600, ...
%t A354402 Table[Sum[(-1)^(k + 1)/(k k!), {k, 1, n}], {n, 1, 20}] // Numerator
%t A354402 nmax = 20; Assuming[x > 0, CoefficientList[Series[(EulerGamma + Log[x] - ExpIntegralEi[-x])/(1 - x), {x, 0, nmax}], x]] // Numerator // Rest
%o A354402 (PARI) a(n) = numerator(sum(k=1, n, (-1)^(k+1)/(k*k!))); \\ _Michel Marcus_, May 26 2022
%o A354402 (Python)
%o A354402 from math import factorial
%o A354402 from fractions import Fraction
%o A354402 def A354402(n): return sum(Fraction(1 if k & 1 else -1, k*factorial(k)) for k in range(1,n+1)).numerator # _Chai Wah Wu_, May 27 2022
%Y A354402 Cf. A001563, A053557, A061354, A103816, A120265, A239069, A353545, A354404 (denominators).
%K A354402 nonn,frac
%O A354402 1,2
%A A354402 _Ilya Gutkovskiy_, May 25 2022