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A015022 q-factorial numbers for q=-8.

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%I A015022 #29 Aug 10 2025 02:40:01
%S A015022 1,1,-7,-399,181545,661005345,-19253102683815,-4486300228074519855,
%T A015022 8363069275661695069900425,124719129516554187174725699959425,
%U A015022 -14879571721119777957252576955487113947975,-14201616428474592152386976225370375696382583866575
%N A015022 q-factorial numbers for q=-8.
%H A015022 Vincenzo Librandi, <a href="/A015022/b015022.txt">Table of n, a(n) for n = 0..40</a>
%H A015022 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A015022 a(n) = Product_{k=1..n} ((-8)^k - 1) / (-8 - 1).
%F A015022 a(1) = 1, a(n) = ((-8)^n - 1)*a(n-1)/(-9). - _Vincenzo Librandi_, Oct 26 2012
%F A015022 a(n) ~ (-1)^floor(n/2) * c * 8^(n*(n+1)/2) / 9^n, where c = Product_{k>=1} (1 - 1/(-8)^k) = 1.1093440055701933033... . - _Amiram Eldar_, Aug 09 2025
%t A015022 RecurrenceTable[{a[1]==1, a[n]==(((-8)^n - 1) * a[n-1])/(-9)}, a, {n, 15}] (* _Vincenzo Librandi_, Oct 26 2012 *)
%o A015022 (Magma) [n le 1 select 1 else ((-8)^n - 1)*Self(n-1)/(-9): n in [1..13]]; // _Vincenzo Librandi_, Oct 26 2012
%Y A015022 Column k=8 of A384454.
%Y A015022 Cf. A015007.
%K A015022 sign,easy
%O A015022 0,3
%A A015022 _Olivier Gérard_
%E A015022 a(0)=1 prepended by _Seiichi Manyama_, May 30 2025