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 A384262 #15 May 26 2025 07:57:24
%S A384262 1,1,20,504,17160,742560,39070080,2422728000,173059286400,
%T A384262 13995229248000,1264020397516800,126115611484262400,
%U A384262 13776096431889792000,1635195634511530291200,209574860127295703040000,28844656968251942737920000,4243193364951971128258560000,664387519844376163893657600000
%N A384262 a(n) = Product_{k=0..n-1} (3*n+k-2).
%F A384262 a(n) = RisingFactorial(3*n-2,n).
%F A384262 a(n) = n! * [x^n] 1/(1 - x)^(3*n-2).
%F A384262 a(n) = n! * binomial(4*n-3,n).
%F A384262 D-finite with recurrence 3*(3*n-4)*(3*n-5)*a(n) -8*(4*n-5)*(4*n-3)*(2*n-3)*a(n-1)=0. - _R. J. Mathar_, May 26 2025
%o A384262 (PARI) a(n) = prod(k=0, n-1, 3*n+k-2);
%o A384262 (Python)
%o A384262 from sympy import rf
%o A384262 def a(n): return rf(3*n-2, n)
%o A384262 (Sage)
%o A384262 def a(n): return rising_factorial(3*n-2, n)
%Y A384262 Cf. A061924, A384164, A384263.
%Y A384262 Cf. A335647.
%K A384262 nonn,easy
%O A384262 0,3
%A A384262 _Seiichi Manyama_, May 23 2025