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 A354016 #5 May 15 2022 07:30:09
%S A354016 1,1,-2,9,-24,70,-720,5985,-39200,337176,-3628800,40907790,-479001600,
%T A354016 6128488080,-87104969952,1318070979225,-20922789888000,
%U A354016 354250929192160,-6402373705728000,121882099274319384,-2432849766865689600,51041047393559059200
%N A354016 Product_{n>=1} (1 + x^n/n!)^a(n) = exp(x).
%F A354016 a(1) = 1; a(n) = (n-1)! * ((-1)^n + Sum_{d|n, 1 < d < n} d * (-d!)^(-n/d) * a(d)).
%t A354016 nn = 22; f[x_] := Product[(1 + x^n/n!)^a[n], {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Exp[x], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%t A354016 a[1] = 1; a[n_] := a[n] = (n - 1)! ((-1)^n + Sum[d (-d!)^(-n/d) a[d], {d, Divisors[n] ~ Complement ~ {1, n}}]); Table[a[n], {n, 1, 22}]
%Y A354016 Cf. A006973, A137852, A170910, A170911, A353822.
%K A354016 sign
%O A354016 1,3
%A A354016 _Ilya Gutkovskiy_, May 14 2022