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 A365828 #7 Sep 21 2023 08:56:31
%S A365828 1,1,2,3,5,8,12,18,27,39,55,78,108,148,201,270,359,475,623,811,1050,
%T A365828 1351,1728,2201,2789,3517,4418,5527,6887,8553,10585,13055,16055,19685,
%U A365828 24065,29343,35685,43287,52387,63253,76200,91605,109897,131575,157231,187539
%N A365828 Number of strict integer partitions of 2n not containing n.
%F A365828 a(n) = A000009(2n) - A000009(n) + 1.
%e A365828 The a(0) = 1 through a(6) = 12 strict partitions:
%e A365828 () (2) (4) (6) (8) (10) (12)
%e A365828 (3,1) (4,2) (5,3) (6,4) (7,5)
%e A365828 (5,1) (6,2) (7,3) (8,4)
%e A365828 (7,1) (8,2) (9,3)
%e A365828 (5,2,1) (9,1) (10,2)
%e A365828 (6,3,1) (11,1)
%e A365828 (7,2,1) (5,4,3)
%e A365828 (4,3,2,1) (7,3,2)
%e A365828 (7,4,1)
%e A365828 (8,3,1)
%e A365828 (9,2,1)
%e A365828 (5,4,2,1)
%t A365828 Table[Length[Select[IntegerPartitions[2n],UnsameQ@@#&&FreeQ[#,n]&]],{n,0,30}]
%Y A365828 The complement is counted by A111133.
%Y A365828 For non-strict partitions we have A182616, complement A000041.
%Y A365828 A000009 counts strict integer partitions.
%Y A365828 A046663 counts partitions with no submultiset summing to k, strict A365663.
%Y A365828 A365827 counts strict partitions not of length 2, complement A140106.
%Y A365828 Cf. A008967, A035363, A078408, A079122, A231429, A238628, A344415, A365659.
%K A365828 nonn
%O A365828 0,3
%A A365828 _Gus Wiseman_, Sep 20 2023