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 A384242 #13 May 26 2025 05:43:00
%S A384242 1,4,24,168,1056,0,-229824,-7233408,-162860544,-2573835264,0,
%T A384242 2333140153344,131053381595136,4948323499671552,124773727026364416,0,
%U A384242 -256422032696998232064,-20710128948965418074112,-1096668276542495972130816,-37948699305215165278715904,0
%N A384242 a(n) = Product_{k=0..n-1} (4*n-5*k).
%F A384242 a(n) = 5^n * FallingFactorial(4*n/5,n).
%F A384242 a(n) = n! * [x^n] (1 + 5*x)^(4*n/5).
%F A384242 a(n) = 4 * (-1)^(n-1) * A383997(n) for n > 0.
%F A384242 a(5*n) = 0 for n > 0.
%F A384242 D-finite with recurrence a(n) +8*n*(4*n-15)*(4*n-5)*(n-5)*(2*n-5)*a(n-5)=0. - _R. J. Mathar_, May 26 2025
%o A384242 (PARI) a(n) = prod(k=0, n-1, 4*n-5*k);
%o A384242 (Sage)
%o A384242 def a(n): return 5^n*falling_factorial(4*n/5, n)
%Y A384242 Cf. A061924, A343446.
%Y A384242 Cf. A383997.
%K A384242 sign,easy
%O A384242 0,2
%A A384242 _Seiichi Manyama_, May 22 2025