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 A384165 #23 May 22 2025 09:54:29
%S A384165 1,3,48,1287,48384,2340135,138378240,9672183675,780151357440,
%T A384165 71322093677835,7287813911347200,823100991923184975,
%U A384165 101819334240239616000,13690816766440373134575,1988199345147516813312000,310120801435080997013527875,51709528644340997758648320000
%N A384165 a(n) = Product_{k=0..n-1} (3*n+2*k).
%H A384165 Vincenzo Librandi, <a href="/A384165/b384165.txt">Table of n, a(n) for n = 0..200</a>
%F A384165 a(n) = 2^n * RisingFactorial(3*n/2,n).
%F A384165 a(n) = n! * [x^n] 1/(1 - 2*x)^(3*n/2).
%F A384165 a(n) = (3/5) * 2^n * n! * binomial(5*n/2,n) for n > 0.
%t A384165 a[n_]:=Product[(3*n+2*k),{k,0,n-1}]; Table[a[n],{n,0,15}] (* _Vincenzo Librandi_, May 22 2025 *)
%o A384165 (PARI) a(n) = prod(k=0, n-1, 3*n+2*k);
%o A384165 (Sage)
%o A384165 def a(n): return 2^n*rising_factorial(3*n/2, n)
%o A384165 (Python)
%o A384165 from math import prod
%o A384165 def A384165(n): return prod(3*n+i for i in range(0,n<<1,2)) # _Chai Wah Wu_, May 21 2025
%o A384165 (Magma) [1] cat [&*[(3*n + 2*k): k in [0..n-1]]: n in [1..16]]; // _Vincenzo Librandi_, May 22 2025
%Y A384165 Cf. A384164, A384166.
%K A384165 nonn,easy
%O A384165 0,2
%A A384165 _Seiichi Manyama_, May 21 2025