OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
EXAMPLE
The a(1) = 1 through a(4) = 10 sequences:
((1)) ((2)) ((3)) ((4))
((11)) ((21)) ((22))
((111)) ((31))
((1)(2)) ((211))
((2)(1)) ((1111))
((11)(1)) ((1)(3))
((3)(1))
((11)(2))
((21)(1))
((111)(1))
MATHEMATICA
ptnseq[n_]:=Join@@Table[Tuples[IntegerPartitions/@comp], {comp, Join@@Permutations/@IntegerPartitions[n]}];
Table[Length[Select[ptnseq[n], UnsameQ@@#&&GreaterEqual@@Length/@#&]], {n, 0, 10}]
PROG
(PARI)
P(n, y) = {1/prod(k=1, n, 1 - y*x^k + O(x*x^n))}
R(n, v) = {[subst(serlaplace(p), y, 1) | p<-Vec(prod(k=1, #v, (1 + y*x^k + O(x*x^n))^v[k] ))]}
seq(n) = {my(g=P(n, y)); Vec(prod(k=1, n, Ser(R(n, Vec(polcoef(g, k, y), -n))) ))} \\ Andrew Howroyd, Dec 31 2022
CROSSREFS
This is the distinct case of A055887 with weakly decreasing lengths.
This is the distinct case is A141199.
The case of distinct lengths also is A358836.
This is the case of A358906 with weakly decreasing lengths.
A001970 counts multiset partitions of integer partitions.
A063834 counts twice-partitions.
A358830 counts twice-partitions with distinct lengths.
A358901 counts partitions with all distinct Omegas.
A358912 counts sequences of partitions with distinct lengths.
A358914 counts twice-partitions into distinct strict partitions.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 09 2022
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Dec 31 2022
STATUS
approved