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 A387083 #15 Aug 26 2025 05:45:39
%S A387083 1,0,1,6,42,360,3690,44100,602280,9253440,157966200,2966317200,
%T A387083 60765843600,1348539192000,32229405608400,825285553092000,
%U A387083 22541609025936000,654175871661312000,20101465198839024000,651991603501798560000,22260385752292527840000
%N A387083 Expansion of e.g.f. (2*(1-x)^2)/(2-4*x+x^2).
%C A387083 For n > 0, a(n) is the number of ways to sit n people around circular tables, choose 2 people from each table, and linear order the tables.
%F A387083 For n > 0, a(n) = ((1 + sqrt(2))^(n-1) - (sqrt(2) - 1)^(n-1)) * n! / 2^(n/2 + 1). - _Vaclav Kotesovec_, Aug 18 2025
%F A387083 D-finite with recurrence 2*a(n) -4*n*a(n-1) +n*(n-1)*a(n-2)=0. - _R. J. Mathar_, Aug 26 2025
%F A387083 a(n) = A060995(n)*n!/2^n. - _R. J. Mathar_, Aug 26 2025
%e A387083 a(6)=3690 since for 6 people the number of ways to do the combined tasks in the comment are: 1800 using one table, 1080 using two tables with 4 and 2 people, 720 using two tables with 3 people each, and 90 using three tables with 2 people each.
%t A387083 With[{m = 20}, CoefficientList[Series[(2*(1 - x)^2)/(2 - 4*x + x^2), {x, 0, m}], x] * Table[n!, {n, 0, m}]] (* _Amiram Eldar_, Aug 16 2025 *)
%Y A387083 Cf. A001286.
%K A387083 nonn,new
%O A387083 0,4
%A A387083 _Enrique Navarrete_, Aug 16 2025