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A336342
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Number of ways to choose a partition of each part of a strict composition of n.
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15
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1, 1, 2, 7, 11, 29, 81, 155, 312, 708, 1950, 3384, 7729, 14929, 32407, 81708, 151429, 305899, 623713, 1234736, 2463743, 6208978, 10732222, 22487671, 43000345, 86573952, 160595426, 324990308, 744946690, 1336552491, 2629260284, 5050032692, 9681365777
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OFFSET
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0,3
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COMMENTS
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A strict composition of n is a finite sequence of distinct positive integers summing to n.
Is there a simple generating function?
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LINKS
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FORMULA
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EXAMPLE
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The a(1) = 1 through a(4) = 11 ways:
(1) (2) (3) (4)
(1,1) (2,1) (2,2)
(1,1,1) (3,1)
(1),(2) (1),(3)
(2),(1) (2,1,1)
(1),(1,1) (3),(1)
(1,1),(1) (1,1,1,1)
(1),(2,1)
(2,1),(1)
(1),(1,1,1)
(1,1,1),(1)
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MATHEMATICA
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Table[Length[Join@@Table[Tuples[IntegerPartitions/@ctn], {ctn, Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&]}]], {n, 0, 10}]
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PROG
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(PARI) seq(n)={[subst(serlaplace(p), y, 1) | p<-Vec(prod(k=1, n, 1 + y*x^k*numbpart(k) + O(x*x^n)))]} \\ Andrew Howroyd, Apr 16 2021
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CROSSREFS
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Multiset partitions of partitions are A001970.
Splittings of partitions are A323583.
Splittings of partitions with distinct sums are A336131.
Partitions:
- Partitions of each part of a partition are A063834.
- Compositions of each part of a partition are A075900.
- Strict partitions of each part of a partition are A270995.
- Strict compositions of each part of a partition are A336141.
Strict partitions:
- Partitions of each part of a strict partition are A271619.
- Compositions of each part of a strict partition are A304961.
- Strict partitions of each part of a strict partition are A279785.
- Strict compositions of each part of a strict partition are A336142.
Compositions:
- Partitions of each part of a composition are A055887.
- Compositions of each part of a composition are A133494.
- Strict partitions of each part of a composition are A304969.
- Strict compositions of each part of a composition are A307068.
Strict compositions:
- Partitions of each part of a strict composition are A336342.
- Compositions of each part of a strict composition are A336127.
- Strict partitions of each part of a strict composition are A336343.
- Strict compositions of each part of a strict composition are A336139.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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