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 A384259 #11 May 26 2025 07:15:26
%S A384259 1,4,45,840,21945,737280,30282525,1470268800,82380323025,
%T A384259 5231974809600,371413503586125,29144138639616000,2504851570980383625,
%U A384259 234017443515727872000,23613335889752371888125,2559272716623604101120000,296519181502679448839150625,36572320958219876869079040000
%N A384259 a(n) = Product_{k=0..n-1} (n+4*k+3).
%F A384259 a(n) = 4^n * RisingFactorial((n+3)/4,n).
%F A384259 a(n) = n! * [x^n] 1/(1 - 4*x)^((n+3)/4).
%F A384259 D-finite with recurrence a(n) -5*(5*n-9)*(5*n-13)*(5*n-1)*(5*n-17)*a(n-4)=0. - _R. J. Mathar_, May 26 2025
%o A384259 (PARI) a(n) = prod(k=0, n-1, n+4*k+3);
%o A384259 (Sage)
%o A384259 def a(n): return 4^n*rising_factorial((n+3)/4, n)
%Y A384259 Cf. A303487, A384258.
%K A384259 nonn,easy
%O A384259 0,2
%A A384259 _Seiichi Manyama_, May 23 2025