A015015 q-factorial numbers for q=-3.

1, 1, -2, -14, 280, 17080, -3108560, -1700382320, 2788627004800, 13722833490620800, -202576467988544249600, -8971504037808659182035200, 1191954026463258458925196672000, 475090227821752019816863814722432000, -568085339196037403679856371543830284544000, -2037851067068183667490280132124059680133919488000

Offset: 0

Author

Olivier Gérard

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..60
• Index entries for sequences related to factorial numbers.

Crossrefs

Column k=3 of A384454.

Cf. A015001.

Programs

Magma

[n le 1 select 1 else ((-3)^n - 1)*Self(n-1)/(-4): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-3)^n - 1) * a[n-1])/(-4)}, a, {n, 18}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-3)^k - 1)/(-3 - 1).

a(1) = 1, a(n) = ((-3)^n - 1)*a(n-1)/(-4). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 3^(n*(n+1)/2) / 4^n, where c = Product_{k>=1} (1 - 1/(-3)^k) = 1.2176479365615020492... . - Amiram Eldar, Aug 09 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 30 2025