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 A384241 #11 May 23 2025 10:20:55
%S A384241 1,3,12,45,0,-3465,-60480,-626535,0,204417675,6227020800,104928949125,
%T A384241 0,-77849405258625,-3379030566912000,-78792721832199375,0,
%U A384241 104312208642352585875,5875458349746585600000,174954117301479619228125,0,-362526128354588965187045625,-25100240092118201519308800000
%N A384241 a(n) = Product_{k=0..n-1} (3*n-4*k).
%F A384241 a(n) = 4^n * FallingFactorial(3*n/4,n).
%F A384241 a(n) = n! * [x^n] (1 + 4*x)^(3*n/4).
%F A384241 a(n) = 3 * (-1)^(n-1) * A383996(n) for n > 0.
%F A384241 a(4*n) = 0 for n > 0.
%o A384241 (PARI) a(n) = prod(k=0, n-1, 3*n-4*k);
%o A384241 (Sage)
%o A384241 def a(n): return 4^n*falling_factorial(3*n/4, n)
%Y A384241 Cf. A064352, A343445.
%Y A384241 Cf. A383996, A384166.
%K A384241 sign,easy
%O A384241 0,2
%A A384241 _Seiichi Manyama_, May 22 2025