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 A323719 #8 Jan 27 2019 18:02:29
%S A323719 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,3,1,1,1,1,2,1,4,1,1,1,1,1,3,1,5,1,
%T A323719 1,1,1,3,1,4,1,6,1,1,1,1,2,6,1,5,1,7,1,1,1,1,2,3,10,1,6,1,8,1,1,1,1,1,
%U A323719 3,4,15,1,7,1,9,1,1,1,1,4,1,4,5,21,1,8,1,10,1,1,1
%N A323719 Array read by antidiagonals upwards where A(n, k) is the number of orderless factorizations of n with k - 1 levels of parentheses.
%C A323719 An orderless factorization of n with k > 1 levels of parentheses is any multiset partition of an orderless factorization of n with k - 1 levels of parentheses. If k = 1 it is just an orderless factorization of n into factors > 1.
%e A323719 Array begins:
%e A323719 k=0 k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9 k=10 k=11 k=12
%e A323719 n=1: 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A323719 n=2: 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A323719 n=3: 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A323719 n=4: 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A323719 n=5: 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A323719 n=6: 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A323719 n=7: 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A323719 n=8: 1 3 6 10 15 21 28 36 45 55 66 78 91
%e A323719 n=9: 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A323719 n=10: 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A323719 n=11: 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A323719 n=12: 1 4 9 16 25 36 49 64 81 100 121 144 169
%e A323719 n=13: 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A323719 n=14: 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A323719 n=15: 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A323719 n=16: 1 5 14 30 55 91 140 204 285 385 506 650 819
%e A323719 n=17: 1 1 1 1 1 1 1 1 1 1 1 1 1
%e A323719 n=18: 1 4 9 16 25 36 49 64 81 100 121 144 169
%e A323719 The A(12,3) = 16 orderless factorizations of 12 with 2 levels of parentheses:
%e A323719 ((2*2*3)) ((2*6)) ((3*4)) ((12))
%e A323719 ((2)*(2*3)) ((2)*(6)) ((3)*(4))
%e A323719 ((3)*(2*2)) ((2))*((6)) ((3))*((4))
%e A323719 ((2))*((2*3))
%e A323719 ((2)*(2)*(3))
%e A323719 ((3))*((2*2))
%e A323719 ((2))*((2)*(3))
%e A323719 ((3))*((2)*(2))
%e A323719 ((2))*((2))*((3))
%t A323719 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A323719 lev[n_,k_]:=If[k==0,{n},Join@@Table[Union[Sort/@Tuples[lev[#,k-1]&/@fac]],{fac,facs[n]}]];
%t A323719 Table[Length[lev[sum-k,k]],{sum,12},{k,0,sum-1}]
%Y A323719 Columns: A001055 (k=1), A050336 (k=2), A050338 (k=3), A050340 (k=4).
%Y A323719 Rows: A000027, A000217, A000290, etc.
%Y A323719 Cf. A096751, A141268, A144150, A213427, A255906, A281113, A290353, A292504, A317145, A318564, A318565, A318812, A323718.
%K A323719 nonn,tabl
%O A323719 1,12
%A A323719 _Gus Wiseman_, Jan 25 2019