A330456 Number of multisets of nonempty sets of nonempty sets of positive integers with total sum n.

1, 1, 2, 5, 10, 20, 43, 84, 168, 332, 650, 1255, 2428, 4636, 8827, 16702, 31457, 58919, 109977, 204286, 378135, 697240, 1281315, 2346612, 4284654, 7799248, 14157079, 25626996, 46269838, 83330373, 149717844, 268371413, 479996794, 856661792, 1525761119, 2712050472

Offset

0,3

Links

Table of n, a(n) for n=0..35.

Formula

Euler transform of A050342. 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) = 10 partitions:
  ((4))  ((13))      ((1)(12))        ((2))((2))  ((1))((1))((1))((1))
         ((1)(3))    ((1))((12))
         ((1))((3))  ((1))((1)(2))
                     ((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[And@@UnsameQ@@@#, And@@UnsameQ@@@Join@@#]&]], {n, 0, 10}]

Crossrefs

Cf. A001055, A001970, A007713, A050342, A050343, A063834, A089259, A270995, A279785, A330461, A323787-A323795, A330452-A330459.

Sequence in context: A267589 A006836 A129847 * A352120 A176692 A212951

Adjacent sequences: A330453 A330454 A330455 * A330457 A330458 A330459

Keyword

nonn

Author

Gus Wiseman, Dec 17 2019

Status

approved