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 A362565 #10 May 15 2023 08:43:16
%S A362565 1,24,532224,237124952064,765985681152147456,
%T A362565 10915755547826792536473600,510278911920303453316871670988800,
%U A362565 64243535333922263307871175411271676723200,18920767554543625469992819764324607588052867481600
%N A362565 The number of linear extensions of n fork-join DAGs of width 4.
%C A362565 The fork-join structure is a modeling structure, commonly seen for example in parallel computing, usually represented as a DAG (or poset). It has an initial "fork" vertex that spawns a number of m independent children vertices (the width) whose output edges are connected to a final "join" vertex. More generally, we can have a number n of these DAGs, each one with m+2 vertices.
%C A362565 When the width is 4 (i.e., m=4), these fork-join DAGs can be depicted as follows (we omit the first column for n=0 because the graph is empty in this case):
%C A362565 n | 1 | 2 | 3
%C A362565 ------------------------------------------------------------
%C A362565 | o | o o | o o o
%C A362565 | /| |\ | /| |\ /| |\ | /| |\ /| |\ /| |\
%C A362565 | o o o o | o o o o o o o o | o o o o o o o o o o o o
%C A362565 | \| |/ | \| |/ \| |/ | \| |/ \| |/ \| |/
%C A362565 | o | o o | o o o
%H A362565 Wikipedia, <a href="https://en.wikipedia.org/wiki/Fork-join_model">Fork-join model</a>.
%F A362565 a(n) = (6n)!/30^n.
%e A362565 a(1) = 24 is the number of linear extensions of one fork-join DAG of width 4.
%t A362565 a[n_] := (6n)!/30^n
%t A362565 Table[a[n], {n, 0, 8}]
%Y A362565 Row m=4 of A357297.
%K A362565 nonn
%O A362565 0,2
%A A362565 _José E. Solsona_, Apr 24 2023