%I #18 Aug 09 2021 10:13:50
%S 1,1,2,6,48,1440,414720,2090188800,1155790798848000,
%T 226483217146419609600000,302971317675145105975227187200000000,
%U 37917003542135076706761224377027811868672000000000000,45800346382799680410294841758069930049013501333211737122406400000000000000000
%N Product over all partitions lambda of n of the product of distinct parts in lambda.
%H Alois P. Heinz, <a href="/A346788/b346788.txt">Table of n, a(n) for n = 0..20</a>
%F a(n) = A230053(n) for n <= 6.
%p a:= n-> mul(i, i=map(x-> {x[]}[], combinat[partition](n))):
%p seq(a(n), n=0..12);
%t a[n_] := Times @@ Times @@@ Union /@ IntegerPartitions[n];
%t a /@ Range[0, 20] (* _Jean-François Alcover_, Aug 09 2021 *)
%o (PARI) a(n) = vecprod(apply(x->vecprod(Set(x)), partitions(n))); \\ _Michel Marcus_, Aug 04 2021
%Y Cf. A000142, A007870, A162506, A230053, A325504.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Aug 03 2021