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 A275289 #12 Jun 20 2025 11:12:35
%S A275289 1,2,7,19,56,160,463,1337,3874,11241,32682,95172,277577,810706,
%T A275289 2370839,6941473,20345618,59692831,175295996,515217034,1515478535,
%U A275289 4460940067,13140081770,38729776774,114221851951,337050020750,995097461503,2939337252651,8686270661400
%N A275289 Number of set partitions of [n] with symmetric block size list of length three.
%H A275289 Alois P. Heinz, <a href="/A275289/b275289.txt">Table of n, a(n) for n = 3..1000</a>
%H A275289 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A275289 G.f.: -(1/2)*(3*x-1+sqrt((1-3*x)*(x+1)*(2*x-1)^2))/((3*x-1)*(x+1)).
%F A275289 a(n) ~ 3^(n-1/2) / (4*sqrt(Pi*n)). - _Vaclav Kotesovec_, Aug 02 2016
%F A275289 Recurrence: (n-3)*n*a(n) = (n^2 - 3*n + 4)*a(n-1) + (n-2)*(5*n - 11)*a(n-2) + 3*(n-3)*(n-2)*a(n-3). - _Vaclav Kotesovec_, Aug 02 2016
%F A275289 From _Mélika Tebni_, Jun 20 2025: (Start)
%F A275289 a(n) = Sum_{k=floor(n/2)..n-2} binomial(n-1, k+1)*binomial(k, n-(k+1)).
%F A275289 Inverse binomial transform of A371965. (End)
%Y A275289 Column k=3 of A275281.
%K A275289 nonn
%O A275289 3,2
%A A275289 _Alois P. Heinz_, Jul 22 2016