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 A105658 #19 Jan 18 2025 19:31:36
%S A105658 1,1,1,3,2,5,3,7,4,9,5,11,6,143,7,15,104,935,9,19,10,21,11,4025,3900,
%T A105658 325,3289,27,14,29,15,31,368,33,17,35,18,185,19,39,380,451,399,215,
%U A105658 770,45,23,29563,24,12397,725,51,26,1537,837,2365,1036,285,377,2537,30
%N A105658 a(n) = (Product_{i=1..n} i^i) / denominator( Sum_{j=1..n} j*(j+1)/2 / (Product_{k=0..j-1} j!/k!) ).
%C A105658 Most of the time a(2n-1)=2n-1, but a(2n-1)!=2n-1 for 2n-1 = 13,17,23,25,37,41,43,47,49,53,55,57,59,61,63,...
%C A105658 Most of the time a(2n)=n, but a(2n)!=n for 2n = 16,24,26,32,40,42,44,50,54,56,58,64,84,86,96,100,102,104,...
%e A105658 a(3) = 108/36 = 3.
%t A105658 f[n_] := Product[k^k, {k, 1, n}]/ Denominator[Sum[i(i + 1)/2/Product[i!/j!, {j, 0, i - 1}], {i, n}]]; Table[ f[n], {n, 0, 61}] (* _Robert G. Wilson v_, Apr 18 2005 *)
%o A105658 (PARI) a(n) = prod(i=1, n, i^i) / denominator(sum(j=1, n, j*(j+1)/2 / prod(k=0, j-1, j!/k!))) \\ _Jason Yuen_, Jan 18 2025
%Y A105658 Cf. A002109 (hyperfactorial numbers).
%K A105658 nonn
%O A105658 0,4
%A A105658 Jess E. Boling (tdbpeekitup(AT)yahoo.com), Apr 17 2005
%E A105658 Edited by _Robert G. Wilson v_, Apr 18 2005
%E A105658 Name corrected by _Jason Yuen_, Jan 18 2025