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%I #4 Apr 16 2019 15:26:42
%S 0,0,0,0,1,3,3,9,12,19,26,39,47,70,89,115,148,189,235,294,362,450,558,
%T 669,817,980,1197,1421,1709,2012,2429,2836,3380,3961,4699,5433,6457,
%U 7433,8770,10109,11818,13547,15912,18109,21105,24121,27959,31736,36840,41670
%N Number of integer partitions of n with exactly two distinct multiplicities.
%C For example, (32211) has two distinct multiplicities (1 and 2) so is counted under a(9).
%C The Heinz numbers of these partitions are given by A323055.
%e The a(4) = 1 through a(9) = 19 partitions:
%e (211) (221) (411) (322) (332) (441)
%e (311) (3111) (331) (422) (522)
%e (2111) (21111) (511) (611) (711)
%e (2221) (3221) (3222)
%e (3211) (4211) (3321)
%e (4111) (5111) (4221)
%e (22111) (22211) (4311)
%e (31111) (32111) (5211)
%e (211111) (41111) (6111)
%e (221111) (22221)
%e (311111) (32211)
%e (2111111) (33111)
%e (42111)
%e (51111)
%e (321111)
%e (411111)
%e (2211111)
%e (3111111)
%e (21111111)
%t Table[Length[Select[IntegerPartitions[n],Length[Union[Length/@Split[#]]]==2&]],{n,0,30}]
%Y Column k = 2 of A325242. Dominated by A325267.
%Y Cf. A008284, A062770, A071625, A098859, A116608, A244515, A323055, A325244.
%K nonn
%O 0,6
%A _Gus Wiseman_, Apr 15 2019
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