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A015023 q-factorial numbers for q=-9.

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%I A015023 #27 Aug 10 2025 02:39:39
%S A015023 1,1,-8,-584,383104,2262229120,-120223904353280,-57502732780460764160,
%T A015023 247530403723531598578155520,9589835030046843645163231485460480,
%U A015023 -3343768718134086569119429099709242848051200,-10493100546581905859843718978714438348266087953203200
%N A015023 q-factorial numbers for q=-9.
%H A015023 Vincenzo Librandi, <a href="/A015023/b015023.txt">Table of n, a(n) for n = 0..40</a>
%H A015023 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A015023 a(n) = Product_{k=1..n} ((-9)^k - 1) / (-9 - 1).
%F A015023 a(1) = 1, a(n) = (((-9)^n - 1) * a(n-1))/(-10). - _Vincenzo Librandi_, Oct 26 2012
%F A015023 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
%t A015023 RecurrenceTable[{a[1]==1, a[n]==(((-9)^n - 1) * a[n-1])/(-10)}, a, {n, 15}] (* _Vincenzo Librandi_, Oct 26 2012 *)
%o A015023 (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
%Y A015023 Column k=9 of A384454.
%Y A015023 Cf. A015008.
%K A015023 sign,easy
%O A015023 0,3
%A A015023 _Olivier Gérard_
%E A015023 a(0)=1 prepended by _Seiichi Manyama_, May 30 2025