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 A241411 #4 Apr 28 2014 18:35:38
%S A241411 0,0,0,0,0,1,2,4,5,9,12,18,23,37,44,64,80,111,139,185,235,306,380,488,
%T A241411 611,771,956,1191,1472,1823,2238,2748,3345,4098,4967,6025,7279,8797,
%U A241411 10558,12709,15204,18215,21692,25880,30702,36545,43194,51166,60314,71255
%N A241411 Number of partitions of n such that the number of parts having multiplicity >1 is a part and the number of distinct parts is not a part.
%C A241411 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 A241411 a(6) counts these 2 partitions: 411, 3111.
%t A241411 z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; d[p_] := Length[DeleteDuplicates[p]];
%t A241411 Table[Count[f[n], p_ /; MemberQ[p, e[p]]], {n, 0, z}] (* A241408 *)
%t A241411 Table[Count[f[n], p_ /; MemberQ[p, e[p]] && MemberQ[p, d[p]]], {n, 0, z}] (* A241409 *)
%t A241411 Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && MemberQ[p, d[p]] ], {n, 0, z}] (* A241410 *)
%t A241411 Table[Count[f[n], p_ /; MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241411 *)
%t A241411 Table[Count[f[n], p_ /; ! MemberQ[p, e[p]] && ! MemberQ[p, d[p]] ], {n, 0, z}] (* A241412 *)
%Y A241411 Cf. A241408, A241409, A241410, A241412.
%K A241411 nonn,easy
%O A241411 0,7
%A A241411 _Clark Kimberling_, Apr 22 2014