%I
%S 1,0,2,2,3,3,7,7,12,15,23,32,42,56,78,100,133,174,224,292,375,479,614,
%T 783,978,1236,1545,1925,2386,2963,3640,4494,5497,6731,8201,9994,12098,
%U 14673,17698,21339,25632,30788,36816,44035,52480,62504,74253,88133,104307
%N Number of partitions p of n such that the number of parts is not a part and max(p)  min(p) is not a part.
%F a(n) + A241386(n) = A000041(n) for n >= 0.
%e a(6) counts these 7 partitions: 6, 51, 411, 33, 3111, 222, 111111.
%t z = 40; f[n_] := f[n] = IntegerPartitions[n];
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241382 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241383 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241384 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241385 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Length[p]]  MemberQ[p, Max[p]  Min[p]]], {n, 0, z}] (* A241386 *)
%Y Cf. A241382, A241383, A241384, A241386.
%K nonn,easy
%O 0,3
%A _Clark Kimberling_, Apr 21 2014
