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 A343580 #14 Apr 21 2021 14:50:09
%S A343580 1,1,4,18,72,600,2400,29400,117600,1905120,7620480,153679680,
%T A343580 614718720,14841066240,59364264960,1669619952000,6678479808000,
%U A343580 214453407168000,857813628672000,30967071995059200,123868287980236800,4965992272662220800,19863969090648883200
%N A343580 a(n) = abs(A021009(n, floor(n/2))).
%C A343580 Absolute value of the middle coefficient of the Laguerre polynomials.
%H A343580 Wikipedia, <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials">Laguerre polynomials</a>
%F A343580 a(n) = ((-1)^floor(n/2)*n!/floor(n/2)!)*hypergeom([n + 1, -floor(n/2)], [1], 1).
%F A343580 a(n) = binomial(n, floor(n/2))*FallingFactorial(n, n - floor(n/2)).
%t A343580 a[n_] := Abs[Hypergeometric2F1[-Floor[n/2], n+1, 1, 1] n!/Floor[n/2]!];
%t A343580 Table[a[n], {n, 0, 20}]
%o A343580 (SageMath)
%o A343580 def a(n): return binomial(n, n - n//2)*falling_factorial(n, n - n//2)
%o A343580 print([a(n) for n in range(23)])
%o A343580 (PARI) a(n) = abs(n!*polcoef(pollaguerre(n), n\2)); \\ _Michel Marcus_, Apr 21 2021
%Y A343580 Cf. A021009, A295383.
%K A343580 nonn
%O A343580 0,3
%A A343580 _Peter Luschny_, Apr 20 2021