cp's OEIS Frontend

A330454 Number of sets of nonempty sets of nonempty multisets of positive integers with total sum n.

%I A330454 #5 Dec 17 2019 22:04:47
%S A330454 1,1,2,7,15,39,94,224,526,1236,2857,6568,15003,34030,76757,172216,
%T A330454 384386,853960,1888891,4160524,9128355,19953661,43463021,94354292,
%U A330454 204182435,440505489,947590424,2032730905,4348897216,9280361316,19755155955,41953293592,88891338202
%N A330454 Number of sets of nonempty sets of nonempty multisets of positive integers with total sum n.
%F A330454 Weigh transform of A261049. 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 A330454 The a(4) = 15 partitions:
%e A330454   ((4))  ((22))  ((13))      ((112))        ((1111))
%e A330454                  ((1)(3))    ((1)(12))      ((1)(111))
%e A330454                  ((1))((3))  ((2)(11))      ((1))((111))
%e A330454                              ((1))((12))    ((1))((1)(11))
%e A330454                              ((2))((11))
%e A330454                              ((1))((1)(2))
%t A330454 ppl[n_,k_]:=Switch[k,0,{n},1,IntegerPartitions[n],_,Join@@Table[Union[Sort/@Tuples[ppl[#,k-1]&/@ptn]],{ptn,IntegerPartitions[n]}]];
%t A330454 Table[Length[Select[ppl[n,3],And[UnsameQ@@#,And@@UnsameQ@@@#]&]],{n,0,10}]
%Y A330454 Cf. A001970, A007713, A050336, A050342, A050343, A261049, A271619, A279785, A330461, A330463, A323787-A323795, A330452-A330459.
%K A330454 nonn
%O A330454 0,3
%A A330454 _Gus Wiseman_, Dec 17 2019