OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
EXAMPLE
The a(1) = 1 through a(4) = 18 sequences:
((1)) ((2)) ((3)) ((4))
((11)) ((12)) ((13))
((21)) ((22))
((111)) ((31))
((1)(2)) ((112))
((2)(1)) ((121))
((1)(11)) ((211))
((11)(1)) ((1111))
((1)(3))
((3)(1))
((1)(12))
((11)(2))
((1)(21))
((12)(1))
((2)(11))
((21)(1))
((1)(111))
((111)(1))
MAPLE
g:= proc(n) option remember; ceil(2^(n-1)) end:
b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0, (t->
add(binomial(t, j)*b(n-i*j, i-1, p+j), j=0..min(t, n/i)))(g(i))))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..32); # Alois P. Heinz, Dec 15 2022
MATHEMATICA
comps[n_]:=Join@@Permutations/@IntegerPartitions[n];
Table[Length[Select[Join@@Table[Tuples[comps/@c], {c, comps[n]}], UnsameQ@@#&]], {n, 0, 10}]
CROSSREFS
This is the strict case of A133494.
The version for sequences of partitions is A358906.
A001970 counts multiset partitions of integer partitions.
A063834 counts twice-partitions.
A218482 counts sequences of compositions with weakly decreasing lengths.
A358830 counts twice-partitions with distinct lengths.
A358901 counts partitions with all different Omegas.
A358914 counts twice-partitions into distinct strict partitions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 07 2022
EXTENSIONS
a(16)-a(29) from Alois P. Heinz, Dec 15 2022
STATUS
approved