cp's OEIS Frontend

A355390 Number of ordered pairs of distinct integer partitions of n.

%I A355390 #10 Jul 05 2022 06:47:25
%S A355390 0,0,2,6,20,42,110,210,462,870,1722,3080,5852,10100,18090,30800,53130,
%T A355390 87912,147840,239610,392502,626472,1003002,1573770,2479050,3831806,
%U A355390 5931660,9057090,13819806,20834660,31399212,46806122,69697452,102870306,151523790,221488806
%N A355390 Number of ordered pairs of distinct integer partitions of n.
%F A355390 a(n) = 2*A355389(n) = 2*binomial(A000041(n), 2).
%e A355390 The a(0) = 0 through a(3) = 6 pairs:
%e A355390   .  .  (11)(2)  (21)(3)
%e A355390         (2)(11)  (3)(21)
%e A355390                  (111)(3)
%e A355390                  (3)(111)
%e A355390                  (111)(21)
%e A355390                  (21)(111)
%t A355390 Table[Length[Select[Tuples[IntegerPartitions[n],2],UnsameQ@@#&]],{n,0,15}]
%o A355390 (PARI) a(n) = 2*binomial(numbpart(n), 2); \\ _Michel Marcus_, Jul 05 2022
%Y A355390 Without distinctness we have A001255, unordered A086737.
%Y A355390 The version for compositions is A020522, unordered A006516.
%Y A355390 The unordered version is A355389.
%Y A355390 A000041 counts partitions, strict A000009.
%Y A355390 A001970 counts multiset partitions of partitions.
%Y A355390 A063834 counts partitions of each part of a partition.
%Y A355390 Cf. A022811, A070933, A316245, A317715, A319910, A323433, A323583, A339006, A355385.
%K A355390 nonn
%O A355390 0,3
%A A355390 _Gus Wiseman_, Jul 04 2022