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 A323092 #8 Feb 16 2025 08:33:57
%S A323092 1,1,2,2,4,5,7,10,14,17,24,30,40,50,66,81,104,128,161,197,246,300,369,
%T A323092 446,546,656,796,952,1148,1366,1637,1940,2311,2730,3234,3806,4489,
%U A323092 5262,6181,7225,8454,9846,11484,13335,15499,17948,20796,24017,27751,31970,36837
%N A323092 Number of double-free integer partitions of n.
%C A323092 An integer partition is double-free if no part is twice any other part.
%H A323092 Alois P. Heinz, <a href="/A323092/b323092.txt">Table of n, a(n) for n = 0..400</a>
%H A323092 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Double-FreeSet.html">Double-Free Set</a>
%e A323092 The a(1) = 1 through a(8) = 14 double-free integer partitions:
%e A323092 (1) (2) (3) (4) (5) (6) (7) (8)
%e A323092 (11) (111) (22) (32) (33) (43) (44)
%e A323092 (31) (41) (51) (52) (53)
%e A323092 (1111) (311) (222) (61) (62)
%e A323092 (11111) (411) (322) (71)
%e A323092 (3111) (331) (332)
%e A323092 (111111) (511) (431)
%e A323092 (4111) (611)
%e A323092 (31111) (2222)
%e A323092 (1111111) (3311)
%e A323092 (5111)
%e A323092 (41111)
%e A323092 (311111)
%e A323092 (11111111)
%t A323092 Table[Length[Select[IntegerPartitions[n],Intersection[#,2*#]=={}&]],{n,30}]
%Y A323092 Cf. A018819, A051424, A101417, A120641, A276431, A305148, A323093, A323094.
%K A323092 nonn
%O A323092 0,3
%A A323092 _Gus Wiseman_, Jan 04 2019