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Product over all partitions lambda of n of the product of distinct parts in lambda.
1

%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