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 A353822 #5 May 10 2022 14:26:45
%S A353822 0,1,2,9,24,110,720,5985,39200,343224,3628800,41295870,479001600,
%T A353822 6130959120,87104969952,1318070979225,20922789888000,354344089779680,
%U A353822 6402373705728000,121882240625961816,2432849766865689600,51041049953430700800,1124000727777607680000
%N A353822 Product_{n>=1} (1 + x^n/n!)^a(n) = exp(-x)/(1 - x).
%t A353822 nn = 23; f[x_] := Product[(1 + x^n/n!)^a[n], {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Exp[-x]/(1 - x), {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%Y A353822 Cf. A000166, A006973, A137852.
%K A353822 nonn
%O A353822 1,3
%A A353822 _Ilya Gutkovskiy_, May 08 2022