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 A199204 #58 Aug 17 2022 16:21:12
%S A199204 1,1,1,2,2,1,1,2,3,6,6,3,2,1,1,2,3,4,6,8,12,24,24,12,8,6,4,3,2,1,1,2,
%T A199204 3,4,5,6,8,10,12,15,20,24,30,40,60,120,120,60,40,30,24,20,15,12,10,8,
%U A199204 6,5,4,3,2,1
%N A199204 Irregular triangle read by rows: the n-th row being a probability distribution based on n!.
%C A199204 Each row of triangle has 2^(n-1) terms.
%C A199204 The n-th row is built by multiplying the elements of the nonempty subsets of [n-1], sorting, removing the duplicates, and appending the reversed version. Equivalently, the n-th row is also given by the positive divisors of (n-1)! listed in increasing order (A079210), appending the reversed version. - _Stefano Spezia_, Aug 17 2022
%F A199204 A closed form for the sequence is: S_n =(1/n!) Sum {(n-1)!/{(n-1)^i(n-2)^j...2^q 1^r} (ij...qr = 00...00 to 11...11) where ij...qr is a base-2 number whose n-1 digits appear as exponents in the sum.
%e A199204 The first five rows are:
%e A199204 n=2: 1 1
%e A199204 n=3: 1 2 2 1
%e A199204 n=4: 1 2 3 6 6 3 2 1
%e A199204 n=5: 1 2 3 4 6 8 12 24 24 12 8 6 4 3 2 1
%t A199204 Multiply[s_]:=Product[Part[s,i], {i,Length[s]}]; nmax=6; a={}; For[n=2, n<=nmax, n++, b=DeleteDuplicates[Sort[Table[Multiply[Part[Subsets[Drop[Range[n-1], 1]], i]], {i, 2^Length[Range[n-2]]}]]]; AppendTo[a, Join[b, Reverse[b]]]]; a (* or *)
%t A199204 nmax=6; a={};For[n=2,n<=nmax,n++, b=Divisors[(n-1)!]; AppendTo[a,Join[b,Reverse[b]]]]; a (* _Stefano Spezia_, Aug 17 2022 *)
%Y A199204 Cf. A079210.
%K A199204 nonn,tabf
%O A199204 2,4
%A A199204 _Daniel Tisdale_, Nov 03 2011