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 A361865 #10 Jun 30 2025 21:09:30
%S A361865 1,0,3,2,12,18,101,232,1547,3768,24974,116728,687419,3489664,26436217,
%T A361865 159031250,1129056772
%N A361865 Number of set partitions of {1..n} such that the mean of the means of the blocks is an integer.
%e A361865 The set partition y = {{1,4},{2,5},{3}} has block-means {5/2,7/2,3}, with mean 3, so y is counted under a(5).
%e A361865 The a(1) = 1 through a(5) = 12 set partitions:
%e A361865 {{1}} . {{123}} {{1}{234}} {{12345}}
%e A361865 {{13}{2}} {{123}{4}} {{1245}{3}}
%e A361865 {{1}{2}{3}} {{135}{24}}
%e A361865 {{15}{234}}
%e A361865 {{1}{234}{5}}
%e A361865 {{12}{3}{45}}
%e A361865 {{135}{2}{4}}
%e A361865 {{14}{25}{3}}
%e A361865 {{15}{24}{3}}
%e A361865 {{1}{24}{3}{5}}
%e A361865 {{15}{2}{3}{4}}
%e A361865 {{1}{2}{3}{4}{5}}
%t A361865 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]& /@ sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A361865 Table[Length[Select[sps[Range[n]],IntegerQ[Mean[Mean/@#]]&]],{n,6}]
%Y A361865 For median instead of mean we have A361864.
%Y A361865 For sum instead of outer mean we have A361866, median A361911.
%Y A361865 A000110 counts set partitions.
%Y A361865 A067538 counts partitions with integer mean, ranks A326836, strict A102627.
%Y A361865 A308037 counts set partitions whose block-sizes have integer mean.
%Y A361865 A327475 counts subsets with integer mean, median A000975.
%Y A361865 Cf. A007837, A035470, A038041, A275714, A275780, A326512, A326513, A326521, A326537, A327481.
%K A361865 nonn,more
%O A361865 1,3
%A A361865 _Gus Wiseman_, Apr 04 2023
%E A361865 a(13)-a(17) from _Christian Sievers_, Jun 30 2025