A015017 q-factorial numbers for q=-4.
1, 1, -3, -39, 1989, 407745, -333943155, -1094331718935, 14343405840081045, 752010424789609108305, -157707866234752874148183075, -132294978377551030760819002477575, 443908259132104963309174796130361690725, 5958035886896289829709072930982993020807155425
Offset: 0
Links
Programs
-
Magma
[n le 1 select 1 else ((-4)^n - 1)*Self(n-1)/(-5): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012
-
Mathematica
RecurrenceTable[{a[1]==1, a[n]==(((-4)^n-1) * a[n-1])/(-5)}, a, {n, 18}] (* Vincenzo Librandi, Oct 26 2012 *)
Formula
a(n) = Product_{k=1..n} ((-4)^k - 1) / (-4 - 1).
a(1) = 1, a(n) = ((-4)^n - 1)*a(n-1)/(-5). - Vincenzo Librandi, Oct 26 2012
a(n) ~ (-1)^floor(n/2) * c * 4^(n*(n+1)/2) / 5^n, where c = Product_{k>=1} (1 - 1/(-4)^k) = 1.1864623436704848646... . - Amiram Eldar, Aug 09 2025
Extensions
a(0)=1 prepended by Seiichi Manyama, May 30 2025