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 A364524 #13 Sep 01 2023 04:40:08
%S A364524 1,0,2,18,168,1920,26640,433440,8064000,168739200,3922732800,
%T A364524 100310918400,2798327347200,84569169484800,2752393009766400,
%U A364524 95978067913728000,3569951024640000000,141085196791418880000,5903699220162551808000,260764276201191899136000,12124067910801279713280000
%N A364524 Expansion of e.g.f. (1-x)^3/(1-3x+2x^2-x^3).
%C A364524 a(n) is the number of ways to seat n persons on benches, linear order the benches, and select 2 persons from each bench.
%C A364524 A001804(n) is the number of ways if only 1 bench is used.
%e A364524 a(6)=26640 since the number of ways to seat 6 persons on benches, linear order the benches, and select 2 persons from each bench is the following:
%e A364524 1) benches of type 1234,56: 1440 of these, 8640 ways;
%e A364524 2) benches of type 123,456: 720 of these, 6480 ways;
%e A364524 3) benches of type 12,34,56: 720 of these, 720 ways;
%e A364524 4) benches of type 123456: 720 of these, 10800 ways.
%t A364524 With[{max = 20}, Range[0, max]! * CoefficientList[Series[(1 - x)^3/(1 - 3*x + 2*x^2 - x^3), {x, 0, max}], x]] (* _Amiram Eldar_, Jul 28 2023 *)
%Y A364524 Cf. A001804, A002866.
%K A364524 nonn
%O A364524 0,3
%A A364524 _Enrique Navarrete_, Jul 27 2023