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

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

Links

Table of n, a(n) for n=0..33.

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}]

Crossrefs

Cf. A001970, A007713, A049311, A050343, A063834, A089259, A270995, A318564, A323787-A323795, A330452-A330459.

Sequence in context: A336724 A178941 A178155 * A026396 A176502 A319003

Adjacent sequences: A330454 A330455 A330456 * A330458 A330459 A330460

Keyword

nonn

Author

Gus Wiseman, Dec 17 2019

Status

approved