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 A239498 #14 Jan 28 2022 00:59:47
%S A239498 0,0,1,0,0,2,0,1,3,1,2,5,4,4,8,7,9,15,15,18,23,26,32,43,47,57,72,80,
%T A239498 98,120,138,163,198,227,267,323,372,438,517,596,696,818,944,1098,1282,
%U A239498 1477,1711,1989,2285,2637,3049,3496,4023,4633,5303,6080,6976,7968
%N A239498 Number of partitions p of n such that if h = 2*min(p), then h is an (h,1)-separator of p; see Comments.
%C A239498 Suppose that p is a partition of n into 2 or more parts and that h is a part of p. Then p is (h,0)-separable if there is an ordering x, h, x, h, ..., h, x of the parts of p, where each x represents any part of p except h. Here, the number of h's on the ends of the ordering is 0. Similarly, p is (h,1)-separable if there is an ordering x, h, x, h, ..., x, h, where the number of h's on the ends is 1; next, p is (h,2)-separable if there is an ordering h, x, h, ..., x, h. Finally, p is h-separable if it is (h,i)-separable for i = 0,1,2.
%e A239498 a(9) counts these partitions: 63, 4212, 212121.
%t A239498 z = 35; t1 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Min[p]] == Length[p]], {n, 1, z}] (* A239497 *)
%t A239498 t2 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 2 Min[p]] == Length[p]], {n, 1, z}] (* A239498 *)
%t A239498 t3 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Max[p]] == Length[p]], {n, 1, z}] (* A118096 *)
%t A239498 t4 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Length[p]] == Length[p]], {n, 1, z}] (* A239500 *)
%t A239498 t5 = Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Max[p] - Min[p]] == Length[p]], {n, 1, z}] (* A239501 *)
%Y A239498 Cf. A239497, A118096, A239500, A239501, A239482.
%K A239498 nonn,easy
%O A239498 1,6
%A A239498 _Clark Kimberling_, Mar 24 2014