A015022 q-factorial numbers for q=-8.

1, 1, -7, -399, 181545, 661005345, -19253102683815, -4486300228074519855, 8363069275661695069900425, 124719129516554187174725699959425, -14879571721119777957252576955487113947975, -14201616428474592152386976225370375696382583866575

Offset: 0

Author

Olivier Gérard

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..40
• Index entries for sequences related to factorial numbers.

Crossrefs

Column k=8 of A384454.

Cf. A015007.

Programs

Magma

[n le 1 select 1 else ((-8)^n - 1)*Self(n-1)/(-9): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-8)^n - 1) * a[n-1])/(-9)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-8)^k - 1) / (-8 - 1).

a(1) = 1, a(n) = ((-8)^n - 1)*a(n-1)/(-9). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 8^(n*(n+1)/2) / 9^n, where c = Product_{k>=1} (1 - 1/(-8)^k) = 1.1093440055701933033... . - Amiram Eldar, Aug 09 2025

Extensions

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