A015027 q-factorial numbers for q=-12.

1, 1, -11, -1463, 2333485, 44665236385, -10259202810507035, -28277368892180867021255, 935288538953861649874525071325, 371221802129246962654056875248358359825, -1768082733073463162105209099485375242162416580075, -101053866980328304416804100016021966697144304636338865493975

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=12 of A384454.

Programs

Magma

[1] cat [n le 1 select 1 else ((-12)^n - 1)*Self(n-1)/(-13): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-12)^n - 1) * a[n-1])/(-13)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} (q^k - 1) / (q - 1) for q=-12.

a(0) = 1, a(n) = ((-12)^n -1)*a(n-1)/(-13). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 12^(n*(n+1)/2) / 13^n, where c = Product_{k>=1} (1 - 1/(-12)^k) = 1.07638484220489190916... . - Amiram Eldar, Aug 10 2025

Extensions

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