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 A357582 #38 Sep 12 2023 08:32:46
%S A357582 1,2,6,30,154,1105,4788,20677,216931,858925,7105392,5546059,
%T A357582 2018025900,1480452337,3238556831,107972737,18425956230000,4683032671,
%U A357582 14053747110612300,160436746661,33809725025123,15260431896321667,1583855315457687090000
%N A357582 a(n) = A061300(n+1)/A061300(n).
%C A357582 It is not known if the ratios A061300(n+1)/A061300(n) are always integer, but so far (for the listed terms) they are. - _Max Alekseyev_, Sep 05 2023
%H A357582 Max Alekseyev, <a href="/A357582/b357582.txt">Table of n, a(n) for n = 0..29</a>
%e A357582 a(5) = 1105 as A061300(5+1) / A061300(5) = 61261200 / 55440 = 1105.
%t A357582 A061300[n_Integer?NonNegative] := A061300[n] = Module[{fact = n!, num = 1}, Monitor[While[Length@Divisors@num != fact, num++]; num, {n, num}]]; a[n_] := A061300[n + 1]/A061300[n]; Table[a[n], {n, 0, 4}] (* _Robert P. P. McKone_, Sep 07 2023 *)
%Y A357582 Cf. A061300.
%K A357582 nonn,hard
%O A357582 0,2
%A A357582 _J. Lowell_, Oct 04 2022
%E A357582 a(11)-a(21) from _David A. Corneth_, Oct 05 2022
%E A357582 a(22)-a(29) from _Max Alekseyev_, Sep 05 2023