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 A288817 #15 Feb 16 2025 08:33:48
%S A288817 1,1,1,3,6,20,67,291,1099,5780,26249,153238,832366,5443440,32738738,
%T A288817 239515824,1591963864,12548347149,93066370414
%N A288817 Number of set partitions of [n] such that each subset is sum-free.
%C A288817 The count can be built constructively by listing all possible sum-free sets of partitions into collections containing {1, ..., n}. For n>1, iterate over the previous generation and insert n into each partition if the result is sum-free, and also append n to the end as its own partition. See Example.
%H A288817 Ben Burns, <a href="/A288817/a288817.cs.txt">C# program to generate counts</a>
%H A288817 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Sum-FreeSet.html">Sum-Free Set</a>
%e A288817 Where "|" is a partition divider, then:
%e A288817 a(1)=1, given by { 1 }.
%e A288817 a(2)=1, given by { 1|2 }.
%e A288817 a(3)=3, given by { 1,3|2 }, { 1|2,3 }, { 1|2|3 }.
%e A288817 a(4)=6, given by { 1,3|2|4 }, { 1,4|2,3 }, { 1|2,3|4 }, { 1,4|2|3 }, { 1|2|3,4 }, { 1|2|3|4 }.
%Y A288817 Cf. A007865, A000041.
%K A288817 nonn,more
%O A288817 0,4
%A A288817 _Ben Burns_, Jun 17 2017