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 A365293 #14 Sep 01 2023 04:40:43
%S A365293 1,1,4,24,192,1800,20880,282240,4354560,75479040,1455148800,
%T A365293 30855686400,713712384000,17884003737600,482619020083200,
%U A365293 13954193180928000,430360865206272000,14102295149150208000,489295008086556672000,17919783031425859584000
%N A365293 a(n) = n!*tetranacci(n+3).
%C A365293 a(n) is the number of ways to partition [n] into blocks of size at most 4, order the blocks, and order the elements within each block.
%F A365293 E.g.f.: 1/(1-x-x^2-x^3-x^4).
%F A365293 a(n) = A000142(n) * A000078(n+3).
%e A365293 a(5) = 1800 since the number of ways to partition [5] into blocks of size at most 4, order the blocks, and order the elements within each block are the following:
%e A365293 1) 1234,5: 10 such ordered blocks; 240 ways;
%e A365293 2) 123,4,5: 60 such ordered blocks; 360 ways;
%e A365293 3) 123,45: 20 such ordered blocks; 240 ways;
%e A365293 4) 12,34,5: 90 such ordered blocks; 360 ways;
%e A365293 5) 12,3,4,5: 240 such ordered blocks; 480 ways;
%e A365293 6) 1,2,3,4,5: 120 such ordered blocks; 120 ways.
%t A365293 Table[n! SeriesCoefficient[1/(1-x-x^2-x^3-x^4),{x,0,n}],{n,0,19}] (* _Stefano Spezia_, Aug 31 2023 *)
%Y A365293 Cf. A000078, A000142, A002866, A005442, A276924, A364324.
%K A365293 nonn
%O A365293 0,3
%A A365293 _Enrique Navarrete_, Aug 31 2023