A015028 q-factorial numbers for q=-13.

1, 1, -12, -1884, 3843360, 101929750560, -35142523960072320, -157510092662430660915840, 9177558663913662855639573043200, 6951672507594336724476921764731548211200, -68453363408439970530162052940526993784438155878400, -8762814767092584880014595182992133840006733019391100715212800

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=13 of A384454.

Programs

Magma

[1] cat [n le 1 select 1 else ((-13)^n - 1)*Self(n-1)/(-14): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-13)^n - 1) a[n-1])/(-14)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-13)^k - 1) / (-13 - 1).

a(0) = 1, a(n) = ((-13)^n - 1)*a(n-1)/(-14). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 13^(n*(n+1)/2) / 14^n, where c = Product_{k>=1} (1 - 1/(-13)^k) = 1.07100320793234536419... . - Amiram Eldar, Aug 10 2025

Extensions

a(0)=1 prepended by Seiichi Manyama, May 31 2025