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 A300335 #19 Aug 30 2024 18:33:14
%S A300335 1,1,2,6,18,65,258,1156,5558,29029,161942,967921,6110687,40807420,
%T A300335 286177944,2107745450,16202590638,130043111849,1085011337141,
%U A300335 9408577992091,84501248359552,786018565954838,7550153439748394
%N A300335 Number of ordered set partitions of {1,...,n} with weakly increasing block-sums.
%e A300335 The a(3) = 6 ordered set partitions: (123), (1)(23), (2)(13), (12)(3), (3)(12), (1)(2)(3).
%t A300335 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A300335 Table[Sum[Times@@Factorial/@Length/@GatherBy[sptn,Total],{sptn,sps[Range[n]]}],{n,8}]
%Y A300335 A000110(n) <= a(n) <= A000670(n).
%Y A300335 Cf. A005651, A063834, A275780, A279375, A279790, A279791, A281113.
%K A300335 nonn,more
%O A300335 0,3
%A A300335 _Gus Wiseman_, Mar 03 2018
%E A300335 a(12)-a(15) from _Alois P. Heinz_, Mar 03 2018
%E A300335 a(16)-a(22) from _Christian Sievers_, Aug 30 2024