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A330455
Number of sets of nonempty multisets of nonempty sets of positive integers with total sum n.
0
1, 1, 2, 6, 12, 28, 62, 134, 285, 610, 1277, 2661, 5506, 11305, 23064, 46803, 94406, 189484, 378522, 752668, 1490319, 2939093, 5774065, 11302564, 22048496, 42869613, 83091843, 160569590, 309398958, 594532990, 1139416396, 2178119059, 4153507514, 7901706341
OFFSET
0,3
FORMULA
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.
EXAMPLE
The a(4) = 12 partitions:
((4)) ((2)(2)) ((13)) ((1)(12)) ((1)(1)(1)(1))
((1)(3)) ((1)(1)(2)) ((1))((1)(1)(1))
((1))((3)) ((1))((12))
((1))((1)(2))
((2))((1)(1))
MATHEMATICA
ppl[n_, k_]:=Switch[k, 0, {n}, 1, IntegerPartitions[n], _, Join@@Table[Union[Sort/@Tuples[ppl[#, k-1]&/@ptn]], {ptn, IntegerPartitions[n]}]];
Table[Length[Select[ppl[n, 3], And[UnsameQ@@#, And@@UnsameQ@@@Join@@#]&]], {n, 0, 10}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 17 2019
STATUS
approved