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q-factorial numbers for q=-6.
1

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

%S 1,-5,-155,28675,31857925,-212333070125,-8491411807368875,

%T 2037471806119124711875,2933289072587326393069793125,

%U -25337824341236140066496699758578125,-1313212585969062194023540996089250607796875

%N q-factorial numbers for q=-6.

%H Vincenzo Librandi, <a href="/A015019/b015019.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) = ((-6)^n - 1)*a(n-1)/(-7). - _Vincenzo Librandi_, Oct 26 2012

%t RecurrenceTable[{a[1]==1, a[n]==(((-6)^n - 1) * a[n-1])/(-7)}, a, {n, 15}] (* _Vincenzo Librandi_, Oct 26 2012 *)

%o (Magma) [n le 1 select 1 else ((-6)^n - 1)*Self(n-1)/(-7): n in [1..18]]; // _Vincenzo Librandi_, Oct 26 2012

%K sign,easy

%O 1,2

%A _Olivier GĂ©rard_