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 A339402 #25 May 27 2022 15:34:53
%S A339402 1,1,1,2,2,3,120,720,1008,40320,362880,45360,39916800,68428800,
%T A339402 6227020800,87178291200,1307674368000,1046139494400,355687428096000,
%U A339402 376610217984000,40548366802944000,2432902008176640000,5676771352412160000,40142883134914560000,25852016738884976640000
%N A339402 a(n) = denominator of (1/e)^n * Sum_{k>=0}(n^k*k^n)/(n!*k!).
%F A339402 A339401(n)/a(n) = A242817(n)/n!. - _Pontus von Brömssen_, Dec 03 2020
%F A339402 a(n) = denominator([x^n] exp(n*(exp(x)-1))). - _Alois P. Heinz_, Dec 07 2020
%p A339402 A:= proc(n, k) option remember; `if`(n=0, 1, (1+
%p A339402 add(binomial(n-1, j-1)*A(n-j, k), j=1..n-1))*k)
%p A339402 end:
%p A339402 a:= n-> denom(A(n$2)/n!):
%p A339402 seq(a(n), n=0..30); # _Alois P. Heinz_, Dec 07 2020
%t A339402 a[n_] := BellB[n, n]/n! // Denominator;
%t A339402 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 27 2022 *)
%Y A339402 Cf. A339401 for numerators and relation to A242817.
%K A339402 nonn,frac
%O A339402 0,4
%A A339402 _William C. Laursen_, Dec 03 2020