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 A299070 #8 Feb 23 2018 11:09:21
%S A299070 1,2,0,3,1,0,5,3,0,0,7,9,0,0,0,13,17,2,0,0,0,19,39,6,0,0,0,0,35,72,21,
%T A299070 0,0,0,0,0,59,141,55,1,0,0,0,0,0,107,266,132,7,0,0,0,0,0,0,187,511,
%U A299070 300,26,0,0,0,0,0,0,0
%N A299070 Regular triangle T(n,k) is the number of compositions of n whose standard factorization into Lyndon words has k distinct factors.
%C A299070 Row sums are 2^(n-1). First column is A008965. A version without the zeros is A299072.
%e A299070 Triangle begins:
%e A299070 1
%e A299070 2 0
%e A299070 3 1 0
%e A299070 5 3 0 0
%e A299070 7 9 0 0 0
%e A299070 13 17 2 0 0 0
%e A299070 19 39 6 0 0 0 0
%e A299070 35 72 21 0 0 0 0 0
%e A299070 59 141 55 1 0 0 0 0 0
%e A299070 107 266 132 7 0 0 0 0 0 0
%e A299070 187 511 300 26 0 0 0 0 0 0 0.
%e A299070 The a(5,2) = 9 compositions are (41), (32), (311), (131), (221), (212), (2111), (1211), (1121) with factorizations
%e A299070 (41) = (4) * (1)
%e A299070 (32) = (3) * (2)
%e A299070 (311) = (3) * (1)^2
%e A299070 (131) = (13) * (1)
%e A299070 (221) = (2)^2 * (1)
%e A299070 (212) = (2) * (12)
%e A299070 (2111) = (2) * (1)^3
%e A299070 (1211) = (12) * (1)^2
%e A299070 (1121) = (112) * (1).
%t A299070 LyndonQ[q_]:=Array[OrderedQ[{q,RotateRight[q,#]}]&,Length[q]-1,1,And]&&Array[RotateRight[q,#]&,Length[q],1,UnsameQ];
%t A299070 qit[q_]:=If[#===Length[q],{q},Prepend[qit[Drop[q,#]],Take[q,#]]]&[Max@@Select[Range[Length[q]],LyndonQ[Take[q,#]]&]];
%t A299070 Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],Length[Union[qit[#]]]===k&]],{n,11},{k,n}]
%Y A299070 Cf. A001045, A001221, A008965, A059966, A116608, A146289, A185700, A296373, A299072.
%K A299070 nonn,tabl
%O A299070 1,2
%A A299070 _Gus Wiseman_, Feb 01 2018