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 A384261 #13 May 26 2025 05:19:53
%S A384261 1,1,12,210,5040,154440,5765760,253955520,12893126400,741354768000,
%T A384261 47621141568000,3379847863392000,262662462526464000,
%U A384261 22183557976419840000,2023140487449489408000,198155371076302768128000,20744817468539834621952000,2311708772421640603275264000
%N A384261 a(n) = Product_{k=0..n-1} (2*n+k-1).
%F A384261 a(n) = RisingFactorial(2*n-1,n).
%F A384261 a(n) = n! * [x^n] 1/(1 - x)^(2*n-1).
%F A384261 a(n) = n! * binomial(3*n-2,n).
%F A384261 D-finite with recurrence 2*(-2*n+3)*a(n) +3*(3*n-2)*(3*n-4)*a(n-1)=0. - _R. J. Mathar_, May 26 2025
%o A384261 (PARI) a(n) = prod(k=0, n-1, 2*n+k-1);
%o A384261 (Python)
%o A384261 from sympy import rf
%o A384261 def a(n): return rf(2*n-1, n)
%o A384261 (Sage)
%o A384261 def a(n): return rising_factorial(2*n-1, n)
%Y A384261 Cf. A064352, A352601.
%Y A384261 Cf. A090816, A117671.
%K A384261 nonn,easy
%O A384261 0,3
%A A384261 _Seiichi Manyama_, May 23 2025