This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A241410 #7 Feb 11 2019 09:32:00
%S A241410 0,1,0,1,0,1,2,2,4,5,7,8,12,17,22,29,33,49,59,77,97,123,153,199,234,
%T A241410 306,375,460,557,708,845,1048,1266,1548,1852,2282,2698,3303,3919,4732,
%U A241410 5634,6786,7991,9598,11343,13502,15897,18912,22180,26298,30775,36259
%N A241410 Number of partitions of n such that the number of parts having multiplicity >1 is not a part and the number of distinct parts is a part.
%C A241410 As used here, the term "distinct parts" includes each number, once, that occurs more than once; e.g., the distinct parts of the partition {4,3,3,1,1,1} are 4, 3, 1.
%e A241410 a(6) counts these 2 partitions: 42, 321.
%t A241410 z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
%t A241410 Table[Count[f[n], p_ /; MemberQ[p, e[p]]], {n, 0, z}] (* A241408 *)
%t A241410 Table[Count[f[n], p_ /; MemberQ[p, e[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241409 *)
%t A241410 Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && MemberQ[p, d[p]] ], {n, 0, z}] (* A241410 *)
%t A241410 Table[Count[f[n], p_ /; MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241411 *)
%t A241410 Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241412 *)
%Y A241410 Cf. A241408, A241409, A241411, A241412.
%K A241410 nonn,easy
%O A241410 0,7
%A A241410 _Clark Kimberling_, Apr 22 2014