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 A330458 #5 Dec 18 2019 09:02:04
%S A330458 1,1,3,8,20,49,123,292,701,1653,3874,8977,20711,47344,107692,243382,
%T A330458 547264,1224048,2725483,6040796,13334354,29316445,64215841,140159357,
%U A330458 304890958,661097630,1429083295,3080159882,6620188725,14190463947,30338920339,64702805452
%N A330458 Number of multisets of nonempty sets of nonempty multisets of positive integers with total sum n.
%F A330458 Euler transform of A261049. 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 A330458 The a(4) = 20 partitions:
%e A330458 ((4)) ((22)) ((13)) ((112)) ((1111))
%e A330458 ((2))((2)) ((1)(3)) ((1)(12)) ((1)(111))
%e A330458 ((1))((3)) ((2)(11)) ((1))((111))
%e A330458 ((1))((12)) ((11))((11))
%e A330458 ((2))((11)) ((1))((1)(11))
%e A330458 ((1))((1)(2)) ((1))((1))((11))
%e A330458 ((1))((1))((2)) ((1))((1))((1))((1))
%t A330458 ppl[n_,k_]:=Switch[k,0,{n},1,IntegerPartitions[n],_,Join@@Table[Union[Sort/@Tuples[ppl[#,k-1]&/@ptn]],{ptn,IntegerPartitions[n]}]];
%t A330458 Table[Length[Select[ppl[n,3],And@@UnsameQ@@@#&]],{n,0,10}]
%Y A330458 Cf. A001970, A007713, A050342, A050343, A063834, A089259, A261049, A270995, A271619, A323787-A323795, A330452-A330459.
%K A330458 nonn
%O A330458 0,3
%A A330458 _Gus Wiseman_, Dec 17 2019