login
q-factorial numbers for q=-11.
1

%I #16 Sep 08 2022 08:44:39

%S 1,-10,-1110,1354200,18174718200,-2683133647866000,

%T -4357223907912681246000,77834136400782124140797040000,

%U 15294068523753116384387488625702640000,-33057395763506647102922925284376653918412000000

%N q-factorial numbers for q=-11.

%H Vincenzo Librandi, <a href="/A015026/b015026.txt">Table of n, a(n) for n = 1..40</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) = ((-11)^n - 1) * a(n-1)/(-12). - _Vincenzo Librandi_, Oct 26 2012

%t RecurrenceTable[{a[1]==1, a[n]==(((-11)^n - 1) a[n-1])/(-12)}, a, {n, 15}] (* _Vincenzo Librandi_, Oct 26 2012 *)

%o (Magma) [n le 1 select 1 else ((-11)^n - 1)*Self(n-1)/(-12): n in [1..13]]; // _Vincenzo Librandi_, Oct 26 2012

%K sign,easy

%O 1,2

%A _Olivier GĂ©rard_