%I
%S 0,0,0,0,0,0,0,0,0,1,1,1,5,2,7,10,15,14,30,28,49,56,81,89,135,148,212,
%T 246,327,377,506,578,759,883,1119,1314,1651,1918,2388,2789,3429,4012,
%U 4880,5688,6883,8029,9618,11213,13388,15550,18464,21431,25316,29343
%N Number of partitions p of n such that the number of distinct parts is not a part and max(p)  min(p) is a part.
%F a(n) + A241387(n) + A241389(n) = A241391(n) for n >= 0.
%e a(9) counts this one partition: 63.
%t z = 40; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]];
%t Table[Count[f[n], p_ /; MemberQ[p, d[p]] && MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241387 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241388 *)
%t Table[Count[f[n], p_ /; MemberQ[p, d[p]] && ! MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241389 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && ! MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241390 *)
%t Table[Count[f[n], p_ /; MemberQ[p, d[p]]  MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241391 *)
%Y Cf. A241387, A241389, A241390, A241391.
%K nonn,easy
%O 0,13
%A _Clark Kimberling_, Apr 21 2014
