A015018 q-factorial numbers for q=-5.

1, 1, -4, -84, 8736, 4551456, -11851991424, -154324780331904, 10047160498728278016, 3270561732706527788046336, -5323179358400075453935368658944, -43320145405426340445710562789228109824, 1762701221841919957075369153792221868461981696, 358622481951075194907281490606356664886183644743663616

Offset: 0

Author

Olivier Gérard

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..50
• Index entries for sequences related to factorial numbers.

Crossrefs

Column k=5 of A384454.

Cf. A015004.

Programs

Magma

[n le 1 select 1 else ((-5)^n - 1)*Self(n-1)/(-6): n in [1..18]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-5)^n - 1) * a[n-1])/(-6)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-5)^k - 1) / (-5 - 1).

a(1) = 1, a(n) = ((-5)^n - 1)*a(n-1)/(-6). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 5^(n*(n+1)/2) / 6^n, where c = Product_{k>=1} (1 - 1/(-5)^k) = 1.1596671959367684201... . - Amiram Eldar, Aug 09 2025

Extensions

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