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.

A053291 Nonsingular n X n matrices over GF(4).

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%I A053291 #31 Jul 06 2025 02:54:42
%S A053291 1,3,180,181440,2961100800,775476766310400,3251791214634074112000,
%T A053291 218210695042457748180566016000,
%U A053291 234298374547168764346587444978647040000,4025200069765920285793155323595159699896401920000,1106437515026051855463365435310419366987397763763798016000000
%N A053291 Nonsingular n X n matrices over GF(4).
%H A053291 Vincenzo Librandi, <a href="/A053291/b053291.txt">Table of n, a(n) for n = 0..40</a>
%F A053291 a(n) = (4^n - 1)*(4^n - 4)*...*(4^n - 4^(n-1)).
%F A053291 a(n) = A053763(n)*A027637(n). - _Bruno Berselli_, Jan 30 2013
%F A053291 From _Amiram Eldar_, Jul 06 2025: (Start)
%F A053291 a(n) = Product_{k=1..n} A115490(k).
%F A053291 a(n) ~ c * 4^(n^2), where c = A100221. (End)
%t A053291 Table[Product[4^n - 4^k, {k,0,n-1}], {n,0,10}] (* _Geoffrey Critzer_, Jan 26 2013 *)
%o A053291 (Magma) [1] cat [&*[(4^n - 4^k): k in [0..n-1]]: n in [1..8]]; // _Bruno Berselli_, Jan 28 2013
%o A053291 (PARI) for(n=0,10, print1(prod(k=0,n-1, 4^n - 4^k), ", ")) \\ _G. C. Greubel_, May 31 2018
%Y A053291 Cf. A002884, A003788, A027637, A053763, A053290, A053292, A053293.
%Y A053291 Cf. A100221, A115490.
%K A053291 nonn,easy
%O A053291 0,2
%A A053291 _Stephen G Penrice_, Mar 04 2000
%E A053291 More terms from _Vladeta Jovovic_, Mar 16 2000