A015026 q-factorial numbers for q=-11.

1, 1, -10, -1110, 1354200, 18174718200, -2683133647866000, -4357223907912681246000, 77834136400782124140797040000, 15294068523753116384387488625702640000, -33057395763506647102922925284376653918412000000, -785971734280677729025139143429963192709390305509012000000

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=11 of A384454.

Cf. A015011.

Programs

Magma

[n le 1 select 1 else ((-11)^n - 1)*Self(n-1)/(-12): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-11)^n - 1) a[n-1])/(-12)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-11)^k - 1) / (-11 - 1).

a(1) = 1, a(n) = ((-11)^n - 1) * a(n-1)/(-12). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 11^(n*(n+1)/2) / 12^n, where c = Product_{k>=1} (1 - 1/(-11)^k) = 1.08263836756981274767... . - Amiram Eldar, Aug 10 2025

Extensions

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