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A015002 q-factorial numbers for q=4. 11

%I #29 Sep 08 2022 08:44:39

%S 1,1,5,105,8925,3043425,4154275125,22686496457625,495586515116818125,

%T 43304845277422684580625,15136126045591163828042953125,

%U 21161832960467051739150680807015625,118345540457280742481284963098558216328125,2647344887069536899904944217513732945696167890625

%N q-factorial numbers for q=4.

%H Vincenzo Librandi, <a href="/A015002/b015002.txt">Table of n, a(n) for n = 0..50</a>

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

%F a(n) = Product_{k=1..n} (q^k - 1) / (q - 1) with q=4.

%F a(0) = 1, a(n) = (4^n-1)*a(n-1)/3. - _Vincenzo Librandi_, Oct 27 2012

%t RecurrenceTable[{a[1]==1, a[n]==((4^n - 1) * a[n-1])/3}, a, {n, 15}] (* _Vincenzo Librandi_, Oct 27 2012 *)

%t Table[QFactorial[n, 4], {n, 15}] (* _Bruno Berselli_, Aug 14 2013 *)

%o (Magma) [n le 1 select 1 else (4^n-1)*Self(n-1)/3: n in [1..15]]; // _Vincenzo Librandi_, Oct 22 2012

%Y Cf. A015001, A015004, A015005, A015006, A015007, A015008, A015009, A015011.

%Y Column q=4 of A069777.

%K nonn,easy

%O 0,3

%A _Olivier GĂ©rard_

%E a(0)=1 prepended by _Alois P. Heinz_, Sep 08 2021

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)