login
A330457
Number of multisets of nonempty multisets of nonempty sets of positive integers with total sum n.
0
1, 1, 3, 7, 17, 37, 87, 187, 414, 887, 1903, 4008, 8437, 17519, 36255, 74384, 151898, 308129, 622269, 1249768, 2499392, 4975421, 9865122, 19481300, 38331536, 75149380, 146840801, 285990797, 555297342, 1074996017, 2075201544, 3995079507, 7671034324, 14692086594
OFFSET
0,3
FORMULA
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.
EXAMPLE
The a(4) = 17 partitions:
((4)) ((13)) ((1)(12)) ((2)(2)) ((1)(1)(1)(1))
((1)(3)) ((1)(1)(2)) ((2))((2)) ((1))((1)(1)(1))
((1))((3)) ((1))((12)) ((1)(1))((1)(1))
((1))((1)(2)) ((1))((1))((1)(1))
((2))((1)(1)) ((1))((1))((1))((1))
((1))((1))((2))
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@@@Join@@#&]], {n, 0, 10}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 17 2019
STATUS
approved