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A330456 Number of multisets of nonempty sets of nonempty sets of positive integers with total sum n. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A176692 A212951 A051109

Adjacent sequences:  A330453 A330454 A330455 * A330457 A330458 A330459

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 17 2019

STATUS

approved

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Last modified October 22 07:53 EDT 2021. Contains 348160 sequences. (Running on oeis4.)