A015025 q-factorial numbers for q=-10.

1, 1, -9, -819, 744471, 6767985861, -615270826637649, -559337171058846967059, 5084883322413411422459366631, 462262120681663158624798004859942421, -420238291486760860506028808179511473194550689, -3820348104463302212917240152587016011603143670290413699

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=10 of A384454.

Cf. A015009.

Programs

Magma

[n le 1 select 1 else ((-10)^n - 1)*Self(n-1)/(-11): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-10)^n - 1) * a[n-1])/(-11)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-10)^k - 1) / (-10 - 1).

a(1) = 1, a(n) = ((-10)^n - 1)*a(n-1)/(-11). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 10^(n*(n+1)/2) / 11^n, where c = Product_{k>=1} (1 - 1/(-10)^k) = 1.0899898999990010... . - Amiram Eldar, Aug 10 2025

Extensions

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