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 A366957 #9 Dec 14 2023 09:34:58
%S A366957 1,0,2,18,24,720,7200,45360,1128960,14152320,199584000,4909766400,
%T A366957 82388275200,1793381990400,47163455539200,1051370191872000,
%U A366957 29396519792640000,863253387988992000,24437860434763776000,807966756915462144000,27000346486744350720000
%N A366957 Expansion of e.g.f. 1/(1-x^2-3*x^3).
%C A366957 For n>0, a(n) is the number of ways to partition [n] into blocks of size at most 3, order the blocks, order the elements within each block, and choose 2 elements from each block.
%C A366957 E.g.: a(6)=7200 since we have the following cases:
%C A366957 12,34,56: 720 such orderings, 1 way to choose two elements from each block;
%C A366957 123,456: 720 such orderings, 3*3 ways to choose two elements from each block;
%C A366957 so 720*1 + 720*9 = 7200 ways.
%t A366957 With[{m = 20}, Range[0, m]! * CoefficientList[Series[1/(1 - x^2 - 3*x^3), {x, 0, m}], x]] (* _Amiram Eldar_, Oct 30 2023 *)
%Y A366957 Cf. A000073, A189886, A364324, A366942, A366950.
%K A366957 nonn
%O A366957 0,3
%A A366957 _Enrique Navarrete_, Oct 30 2023