A015020 q-factorial numbers for q=-7.

1, 1, -6, -258, 77400, 162617400, -2391451484400, -246183190158589200, 177399606828279377520000, 894839274162813664365761520000, -31596243236160097777438406008857120000, -7809512095098558650122990001755435531352160000, 13511712475016607822799577492128185918816231362544000000

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=7 of A384454.

Cf. A015006.

Programs

Magma

[n le 1 select 1 else ((-7)^n - 1)*Self(n-1)/(-8): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-7)^n - 1) * a[n-1])/(-8)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-7)^k - 1) / (-7 - 1).

a(1) = 1, a(n) = ((-7)^n - 1)*a(n-1)/(-8). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 7^(n*(n+1)/2) / 8^n, where c = Product_{k>=1} (1 - 1/(-7)^k) = 1.1223882662358546529... . - Amiram Eldar, Aug 09 2025

Extensions

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