cp's OEIS Frontend

A330457 Number of multisets of nonempty multisets of nonempty sets of positive integers with total sum n.

%I A330457 #5 Dec 18 2019 09:01:56
%S A330457 1,1,3,7,17,37,87,187,414,887,1903,4008,8437,17519,36255,74384,151898,
%T A330457 308129,622269,1249768,2499392,4975421,9865122,19481300,38331536,
%U A330457 75149380,146840801,285990797,555297342,1074996017,2075201544,3995079507,7671034324,14692086594
%N A330457 Number of multisets of nonempty multisets of nonempty sets of positive integers with total sum n.
%F A330457 Euler transform of A089259. 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 A330457 The a(4) = 17 partitions:
%e A330457   ((4))  ((13))      ((1)(12))        ((2)(2))    ((1)(1)(1)(1))
%e A330457          ((1)(3))    ((1)(1)(2))      ((2))((2))  ((1))((1)(1)(1))
%e A330457          ((1))((3))  ((1))((12))                  ((1)(1))((1)(1))
%e A330457                      ((1))((1)(2))                ((1))((1))((1)(1))
%e A330457                      ((2))((1)(1))                ((1))((1))((1))((1))
%e A330457                      ((1))((1))((2))
%t A330457 ppl[n_,k_]:=Switch[k,0,{n},1,IntegerPartitions[n],_,Join@@Table[Union[Sort/@Tuples[ppl[#,k-1]&/@ptn]],{ptn,IntegerPartitions[n]}]];
%t A330457 Table[Length[Select[ppl[n,3],And@@UnsameQ@@@Join@@#&]],{n,0,10}]
%Y A330457 Cf. A001970, A007713, A049311, A050343, A063834, A089259, A270995, A318564, A323787-A323795, A330452-A330459.
%K A330457 nonn
%O A330457 0,3
%A A330457 _Gus Wiseman_, Dec 17 2019