cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A015015 q-factorial numbers for q=-3.

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%I A015015 #32 Aug 10 2025 02:41:34
%S A015015 1,1,-2,-14,280,17080,-3108560,-1700382320,2788627004800,
%T A015015 13722833490620800,-202576467988544249600,-8971504037808659182035200,
%U A015015 1191954026463258458925196672000,475090227821752019816863814722432000,-568085339196037403679856371543830284544000,-2037851067068183667490280132124059680133919488000
%N A015015 q-factorial numbers for q=-3.
%H A015015 Vincenzo Librandi, <a href="/A015015/b015015.txt">Table of n, a(n) for n = 0..60</a>
%H A015015 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A015015 a(n) = Product_{k=1..n} ((-3)^k - 1)/(-3 - 1).
%F A015015 a(1) = 1, a(n) = ((-3)^n - 1)*a(n-1)/(-4). - _Vincenzo Librandi_, Oct 26 2012
%F A015015 a(n) ~ (-1)^floor(n/2) * c * 3^(n*(n+1)/2) / 4^n, where c = Product_{k>=1} (1 - 1/(-3)^k) = 1.2176479365615020492... . - _Amiram Eldar_, Aug 09 2025
%t A015015 RecurrenceTable[{a[1]==1, a[n]==(((-3)^n - 1) * a[n-1])/(-4)}, a, {n, 18}] (* _Vincenzo Librandi_, Oct 26 2012 *)
%o A015015 (Magma) [n le 1 select 1 else ((-3)^n - 1)*Self(n-1)/(-4): n in [1..18]]; // _Vincenzo Librandi_, Oct 26 2012
%Y A015015 Column k=3 of A384454.
%Y A015015 Cf. A015001.
%K A015015 sign,easy
%O A015015 0,3
%A A015015 _Olivier Gérard_
%E A015015 a(0)=1 prepended by _Seiichi Manyama_, May 30 2025