login
q-factorial numbers for q=-4.
1

%I #14 Sep 08 2022 08:44:39

%S 1,-3,-39,1989,407745,-333943155,-1094331718935,14343405840081045,

%T 752010424789609108305,-157707866234752874148183075,

%U -132294978377551030760819002477575,443908259132104963309174796130361690725

%N q-factorial numbers for q=-4.

%H Vincenzo Librandi, <a href="/A015017/b015017.txt">Table of n, a(n) for n = 1..50</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%F Prod_{k=1}^{n} (q^k - 1) / (q - 1).

%F a(1) = 1, a(n) = ((-4)^n - 1)*a(n-1)/(-5). - _Vincenzo Librandi_, Oct 26 2012

%t RecurrenceTable[{a[1]==1, a[n]==(((-4)^n-1) * a[n-1])/(-5)}, a, {n, 18}] (* _Vincenzo Librandi_, Oct 26 2012 *)

%o (Magma) [n le 1 select 1 else ((-4)^n - 1)*Self(n-1)/(-5): n in [1..18]]; // _Vincenzo Librandi_, Oct 26 2012

%K sign,easy

%O 1,2

%A _Olivier GĂ©rard_