A015023 q-factorial numbers for q=-9.

1, 1, -8, -584, 383104, 2262229120, -120223904353280, -57502732780460764160, 247530403723531598578155520, 9589835030046843645163231485460480, -3343768718134086569119429099709242848051200, -10493100546581905859843718978714438348266087953203200

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=9 of A384454.

Cf. A015008.

Programs

Magma

I:=[1]; [n le 1 select I[n] else (((-9)^n - 1) * Self(n-1))/(-10): n in [1..13]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==(((-9)^n - 1) * a[n-1])/(-10)}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)

Formula

a(n) = Product_{k=1..n} ((-9)^k - 1) / (-9 - 1).

a(1) = 1, a(n) = (((-9)^n - 1) * a(n-1))/(-10). - Vincenzo Librandi, Oct 26 2012

a(n) ~ (-1)^floor(n/2) * c * 9^(n*(n+1)/2) / 10^n, where c = Product_{k>=1} (1 - 1/(-9)^k) = 1.098748287932263023... . - Amiram Eldar, Aug 09 2025

Extensions

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