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 A330456 #4 Dec 18 2019 09:01:48
%S A330456 1,1,2,5,10,20,43,84,168,332,650,1255,2428,4636,8827,16702,31457,
%T A330456 58919,109977,204286,378135,697240,1281315,2346612,4284654,7799248,
%U A330456 14157079,25626996,46269838,83330373,149717844,268371413,479996794,856661792,1525761119,2712050472
%N A330456 Number of multisets of nonempty sets of nonempty sets of positive integers with total sum n.
%F A330456 Euler transform of A050342. The Euler transform of a sequence (s_1, s_2, ...) is the sequence with generating function Product_{i > 0} 1/(1 - x^i)^s_i.
%e A330456 The a(4) = 10 partitions:
%e A330456 ((4)) ((13)) ((1)(12)) ((2))((2)) ((1))((1))((1))((1))
%e A330456 ((1)(3)) ((1))((12))
%e A330456 ((1))((3)) ((1))((1)(2))
%e A330456 ((1))((1))((2))
%t A330456 ppl[n_,k_]:=Switch[k,0,{n},1,IntegerPartitions[n],_,Join@@Table[Union[Sort/@Tuples[ppl[#,k-1]&/@ptn]],{ptn,IntegerPartitions[n]}]];
%t A330456 Table[Length[Select[ppl[n,3],And[And@@UnsameQ@@@#,And@@UnsameQ@@@Join@@#]&]],{n,0,10}]
%Y A330456 Cf. A001055, A001970, A007713, A050342, A050343, A063834, A089259, A270995, A279785, A330461, A323787-A323795, A330452-A330459.
%K A330456 nonn
%O A330456 0,3
%A A330456 _Gus Wiseman_, Dec 17 2019