A346788 Product over all partitions lambda of n of the product of distinct parts in lambda.

1, 1, 2, 6, 48, 1440, 414720, 2090188800, 1155790798848000, 226483217146419609600000, 302971317675145105975227187200000000, 37917003542135076706761224377027811868672000000000000, 45800346382799680410294841758069930049013501333211737122406400000000000000000

Offset: 0

Author

Alois P. Heinz, Aug 03 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20

Crossrefs

Cf. A000142, A007870, A162506, A230053, A325504.

Programs

Maple

a:= n-> mul(i, i=map(x-> {x[]}[], combinat[partition](n))):
seq(a(n), n=0..12);

Mathematica

a[n_] := Times @@ Times @@@ Union /@ IntegerPartitions[n];
a /@ Range[0, 20] (* Jean-François Alcover, Aug 09 2021 *)

PARI

a(n) = vecprod(apply(x->vecprod(Set(x)), partitions(n))); \\ Michel Marcus, Aug 04 2021

Formula

a(n) = A230053(n) for n <= 6.