A015002 q-factorial numbers for q=4.

1, 1, 5, 105, 8925, 3043425, 4154275125, 22686496457625, 495586515116818125, 43304845277422684580625, 15136126045591163828042953125, 21161832960467051739150680807015625, 118345540457280742481284963098558216328125, 2647344887069536899904944217513732945696167890625

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..50
• Index entries for sequences related to factorial numbers.

Crossrefs

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

Column q=4 of A069777.

Cf. A002450, A100221.

Programs

Magma

[n le 1 select 1 else (4^n-1)*Self(n-1)/3: n in [1..15]]; // Vincenzo Librandi, Oct 22 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==((4^n - 1) * a[n-1])/3}, a, {n, 15}] (* Vincenzo Librandi, Oct 27 2012 *)
Table[QFactorial[n, 4], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)

Formula

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

a(0) = 1, a(n) = (4^n-1)*a(n-1)/3. - Vincenzo Librandi, Oct 27 2012

From Amiram Eldar, Jul 05 2025: (Start)

a(n) = Product_{k=1..n} A002450(k).

a(n) ~ c * 2^(n*(n+1))/3^n, where c = A100221. (End)

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 08 2021