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 A384263 #17 Sep 04 2025 09:20:07
%S A384263 1,2,30,720,24024,1028160,53721360,3315312000,235989936000,
%T A384263 19033511777280,1715456253772800,170866312333516800,
%U A384263 18638248113733248000,2209723830420986880000,282926061171849199104000,38906746608339829739520000,5719086709283091520696320000,894889312443445445244518400000
%N A384263 a(n) = Product_{k=0..n-1} (3*n+k-1).
%F A384263 a(n) = RisingFactorial(3*n-1,n).
%F A384263 a(n) = n! * [x^n] 1/(1 - x)^(3*n-1).
%F A384263 a(n) = n! * binomial(4*n-2,n).
%F A384263 From _Stefano Spezia_, Sep 04 2025: (Start)
%F A384263 E.g.f.: (1 + 3*hypergeom([-1/4, 1/4, 1/2], [-1/3, 1/3], 2^8*x/3^3])/4.
%F A384263 a(n) ~ 2^(8*n-7)*3^(-3*n-1/2)*exp(-n)*n^(n-1)*(144*n - 13). (End)
%t A384263 a[n_]:=n!*Binomial[4*n-2,n]; Array[a,18,0] (* _Stefano Spezia_, Sep 04 2025 *)
%o A384263 (PARI) a(n) = prod(k=0, n-1, 3*n+k-1);
%o A384263 (Python)
%o A384263 from sympy import rf
%o A384263 def a(n): return rf(3*n-1, n)
%o A384263 (Sage)
%o A384263 def a(n): return rising_factorial(3*n-1, n)
%Y A384263 Cf. A061924, A384164, A384262.
%K A384263 nonn,easy,changed
%O A384263 0,2
%A A384263 _Seiichi Manyama_, May 23 2025