A015019 q-factorial numbers for q=-6.

1, 1, -5, -155, 28675, 31857925, -212333070125, -8491411807368875, 2037471806119124711875, 2933289072587326393069793125, -25337824341236140066496699758578125, -1313212585969062194023540996089250607796875, 408368279891017634352398087776483543777178681171875

Offset: 0

Author

Olivier Gérard

Keywords

• sign
• easy

Links

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

Crossrefs

Column k=6 of A384454.

Cf. A015005.

Programs

Magma

[n le 1 select 1 else ((-6)^n - 1)*Self(n-1)/(-7): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-6)^n - 1) * a[n-1])/(-7)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-6)^k - 1) / (-6 - 1).

a(1) = 1, a(n) = ((-6)^n - 1)*a(n-1)/(-7). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 6^(n*(n+1)/2) / 7^n, where c = Product_{k>=1} (1 - 1/(-6)^k) = 1.1387567153634922027... . - Amiram Eldar, Aug 09 2025

Extensions

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