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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 2 12:48 EST 2023. Contains 360021 sequences. (Running on oeis4.)