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 A342166 #16 Mar 05 2021 06:51:25
%S A342166 1,1,3,39,2925,1582425,7410496275,350464600333575,
%T A342166 191295845123076910125,1355763582602823185129417625,
%U A342166 138623522325287867599380791765497875,224935042709004795568466587349227029537282375,6318777956744220129890735589019782971247629409914638125
%N A342166 Product of first n Fubini numbers.
%H A342166 Wikipedia, <a href="https://en.wikipedia.org/wiki/Ordered_Bell_number">Ordered Bell number</a>
%F A342166 a(n) = Product_{k=1..n} A000670(k).
%F A342166 a(n) ~ c * BarnesG(n+2) / (2^n * log(2)^(n*(n+3)/2)), where c = 0.960303470666951851619546415046950178638511457142008903473074598398282549...
%F A342166 a(n) ~ c * Pi^((n+1)/2) * n^(n^2/2 + n + 5/12) / (A * 2^((n-1)/2) * exp(3*n^2/4 + n - 1/12) * log(2)^(n*(n+3)/2)), where A is the Glaisher-Kinkelin constant A074962.
%p A342166 g:= proc(n) option remember; `if`(n=0, 1,
%p A342166 add(g(n-j)*binomial(n, j), j=1..n))
%p A342166 end:
%p A342166 a:= proc(n) option remember; `if`(n=0, 1, a(n-1)*g(n)) end:
%p A342166 seq(a(n), n=0..15); # _Alois P. Heinz_, Mar 03 2021
%t A342166 Table[Product[Sum[j!*StirlingS2[k, j], {j, 0, k}], {k, 1, n}], {n, 0, 12}]
%t A342166 Table[Product[PolyLog[-k, 1/2]/2, {k, 1, n}], {n, 0, 12}]
%t A342166 FoldList[Times, 1, Table[PolyLog[-n, 1/2]/2, {n, 1, 12}]]
%Y A342166 Cf. A000670, A003046, A003266, A070825, A294373, A342170.
%K A342166 nonn
%O A342166 0,3
%A A342166 _Vaclav Kotesovec_, Mar 03 2021