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 A238589 #18 Jun 19 2025 08:05:14
%S A238589 0,0,1,1,2,4,5,8,13,17,24,36,47,64,88,116,153,203,261,340,439,559,710,
%T A238589 905,1136,1427,1786,2223,2756,3415,4201,5167,6330,7730,9413,11449,
%U A238589 13864,16767,20225,24344,29228,35045,41898,50029,59609,70899,84165,99785,118052
%N A238589 Number of partitions p of n such that 2*min(p) is a part of p.
%H A238589 Alois P. Heinz, <a href="/A238589/b238589.txt">Table of n, a(n) for n = 1..10000</a>
%F A238589 a(n) = A000041(n) - A238594(n).
%F A238589 G.f.: Sum_{k>=1} x^(3*k)/Product_{j>=k} (1-x^j). - _Seiichi Manyama_, May 17 2023
%F A238589 a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*n*sqrt(3)) * (1 - (sqrt(3/2)/Pi + 49*Pi/(24*sqrt(6))) / sqrt(n)). - _Vaclav Kotesovec_, Jun 19 2025
%e A238589 a(6) counts these partitions: 42, 321, 2211, 21111.
%t A238589 Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 2*Min[p]]], {n, 50}]
%o A238589 (PARI) my(N=50, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(3*k)/prod(j=k, N, 1-x^j)))) \\ _Seiichi Manyama_, May 17 2023
%Y A238589 Cf. A117989, A238590, A238591.
%Y A238589 Cf. A118096, A238479, A238594.
%K A238589 nonn,easy
%O A238589 1,5
%A A238589 _Clark Kimberling_, Mar 01 2014