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 A384164 #32 May 24 2025 10:35:29
%S A384164 1,3,42,990,32760,1395360,72681840,4475671200,318073392000,
%T A384164 25622035084800,2306992893004800,229601607198163200,
%U A384164 25028504609870361600,2965681982933429760000,379534960108578193920000,52170410224819317150720000,7666009844358186506465280000,1199151678674216896627654656000
%N A384164 a(n) = Product_{k=0..n-1} (3*n+k).
%H A384164 Vincenzo Librandi, <a href="/A384164/b384164.txt">Table of n, a(n) for n = 0..200</a>
%F A384164 a(n) = RisingFactorial(3*n,n) = A124320(3*n,n) = n! * binomial(4*n-1,n).
%F A384164 a(n) = n! * [x^n] 1/(1 - x)^(3*n).
%F A384164 a(n) = (3/4) * A061924(n) for n > 0.
%t A384164 a[n_]:=Product[(3*n+k),{k,0,n-1}]; Table[a[n],{n,0,15}] (* _Vincenzo Librandi_, May 22 2025 *)
%o A384164 (PARI) a(n) = prod(k=0, n-1, 3*n+k);
%o A384164 (Sage)
%o A384164 def a(n): return rising_factorial(3*n, n)
%o A384164 (Python)
%o A384164 from sympy import rf
%o A384164 def A384164(n): return rf(3*n,n) # _Chai Wah Wu_, May 21 2025
%o A384164 (Magma) [1] cat [&*[(3*n + k): k in [0..n-1]]: n in [1..16]]; // _Vincenzo Librandi_, May 22 2025
%Y A384164 Cf. A384164, A384165.
%Y A384164 Cf. A000407, A352601.
%Y A384164 Cf. A061924, A124320.
%K A384164 nonn,easy
%O A384164 0,2
%A A384164 _Seiichi Manyama_, May 21 2025