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 A225973 #25 Dec 23 2024 14:53:43
%S A225973 1,1,1,2,3,5,6,9,12,16,22,30,39,52,67,84,112,140,176,220,282,336,434,
%T A225973 527,660,798,998,1186,1480,1767,2165,2586,3168,3732,4556,5389,6482,
%U A225973 7654,9211,10789,12937,15153,18037,21086,25060,29159,34527,40172,47301,54927
%N A225973 Number of union-closed partitions of weight n.
%C A225973 The objects being counted are sets of sets of positive integers; each such set is closed under set union, and the sum of all the elements of its elements is n.
%C A225973 The sequence is related to Frankl's notorious union-closed sets conjecture, see the Wikipedia link.
%D A225973 This sequence was proposed by David S. Newman, in a note to the SeqFan mailing list, dated May 19 2013.
%H A225973 Wikipedia, <a href="http://en.wikipedia.org/wiki/Union-closed_sets_conjecture">Union-closed sets conjecture</a>
%H A225973 David S. Newman, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-May/011185.html">Need help calculating</a>
%e A225973 For n = 5, the a(5) = 5 union-closed partitions are: {{5}}, {{4,1}}, {{3,2}}, {{3,1},{1}}, {{2,1},{2}}.
%e A225973 {{3},{2}} has the correct sum, but is not closed under union.
%Y A225973 Cf. A050342 (answers a similar question without the requirement that the sets be closed under union).
%K A225973 nonn
%O A225973 0,4
%A A225973 _Allan C. Wechsler_, May 26 2013