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 A330455 #8 Dec 16 2021 22:31:44
%S A330455 1,1,2,6,12,28,62,134,285,610,1277,2661,5506,11305,23064,46803,94406,
%T A330455 189484,378522,752668,1490319,2939093,5774065,11302564,22048496,
%U A330455 42869613,83091843,160569590,309398958,594532990,1139416396,2178119059,4153507514,7901706341
%N A330455 Number of sets of nonempty multisets of nonempty sets of positive integers with total sum n.
%F A330455 Weigh transform of A089259. The weigh transform of a sequence (s_1, s_2, ...) is the sequence with generating function Product_{i > 0} (1 + x^i)^s_i.
%e A330455 The a(4) = 12 partitions:
%e A330455 ((4)) ((2)(2)) ((13)) ((1)(12)) ((1)(1)(1)(1))
%e A330455 ((1)(3)) ((1)(1)(2)) ((1))((1)(1)(1))
%e A330455 ((1))((3)) ((1))((12))
%e A330455 ((1))((1)(2))
%e A330455 ((2))((1)(1))
%t A330455 ppl[n_,k_]:=Switch[k,0,{n},1,IntegerPartitions[n],_,Join@@Table[Union[Sort/@Tuples[ppl[#,k-1]&/@ptn]],{ptn,IntegerPartitions[n]}]];
%t A330455 Table[Length[Select[ppl[n,3],And[UnsameQ@@#,And@@UnsameQ@@@Join@@#]&]],{n,0,10}]
%Y A330455 Cf. A001055, A001970, A007713, A050336, A050343, A089259, A261049, A270995, A271619, A323787-A323795, A330452-A330459, A330461.
%K A330455 nonn
%O A330455 0,3
%A A330455 _Gus Wiseman_, Dec 17 2019