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 A237752 #14 Jan 25 2022 08:08:49
%S A237752 0,1,1,1,2,3,4,6,7,10,13,18,23,31,39,50,64,82,102,130,162,203,252,313,
%T A237752 384,475,580,710,864,1053,1273,1544,1859,2240,2688,3224,3851,4602,
%U A237752 5476,6514,7727,9160,10826,12791,15072,17747,20853,24481,28679,33577,39231
%N A237752 Number of partitions of n such that 2*(greatest part) <= (number of parts).
%C A237752 Also, the number of partitions of n such that (greatest part) >= 2*(number of parts); hence, the number of partitions of n such that (rank + greatest part) <= 0.
%C A237752 Also, the number of partitions p of n such that max(max(p), 2*(number of parts of p)) is a part of p.
%H A237752 Seiichi Manyama, <a href="/A237752/b237752.txt">Table of n, a(n) for n = 1..1000</a>
%F A237752 a(n) = A000041(n) - A237754(n).
%e A237752 The partitions of 6 that do not qualify are 22311, 21111, 111111, so that a(6) = 11 - 3 = 8.
%t A237752 z = 50; Table[Count[IntegerPartitions[n], p_ /; 2 Max[p] <= Length[p]], {n, z}]
%t A237752 (* also *)
%t A237752 Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Max[Max[p],2*Length[p]]]], {n, 50}]
%Y A237752 Cf. A064173, A237751, A237753-A237757, A000041.
%K A237752 nonn,easy
%O A237752 1,5
%A A237752 _Clark Kimberling_, Feb 13 2014