OFFSET
0,3
COMMENTS
A strict composition of n is a finite sequence of distinct positive integers summing to n.
Is there a simple generating function?
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: Sum_{k>=0} k! * [y^k](Product_{j>=1} 1 + y*x^j*A000041(j)). - Andrew Howroyd, Apr 16 2021
EXAMPLE
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)
MATHEMATICA
Table[Length[Join@@Table[Tuples[IntegerPartitions/@ctn], {ctn, Join@@Permutations/@Select[IntegerPartitions[n], UnsameQ@@#&]}]], {n, 0, 10}]
PROG
(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
CROSSREFS
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.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 18 2020
STATUS
approved