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%I #11 Jan 03 2021 21:12:25
%S 1,1,2,3,5,3,9,9,14,14,18,22,31,27,37,42,65,61,83,82,111,110,142,147,
%T 187,190,230,242,296,319,358,412,471,505,600,595,753,781,895,921,1082,
%U 1143,1272,1405,1587,1632,1872,2000,2263,2419,2648,2799,3223,3319,3723
%N a(n) is the number of integer multisets (partitions) for which the number of partitions of n with matching multiplicity multiset is odd.
%C The number of multiplicity multisets met by a positive even number of partitions of n is A088887(n) - a(n).
%C The parity of a(n) is A040051(n).
%F a(n) = Sum_{k odd} A337583(n, k).
%e The partitions of 7 exhibit 10 = A088887(7) different multisets of multiplicities. Except for (3, 1) (met by partitions (4, 1, 1, 1) and (2, 2, 2, 1)), an odd number of partitions of 7 lead to each of them, so a(7) = 9.
%Y Cf. A088887.
%K nonn
%O 0,3
%A _Álvar Ibeas_, Sep 02 2020