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.
%I A052497 #24 Jul 06 2025 02:56:06
%S A052497 1,8,5760,339655680,1624314979123200,629282246371356907929600,
%T A052497 19747506525777609095698646040576000,
%U A052497 50195501537943419769100848121708339934527488000
%N A052497 Number of nonsingular n X n matrices over GF(9).
%H A052497 G. C. Greubel, <a href="/A052497/b052497.txt">Table of n, a(n) for n = 0..30</a>
%H A052497 Jeffrey Overbey, William Traves, and Jerzy Wojdylo, <a href="https://doi.org/10.1080/0161-110591893771">On the Keyspace of the Hill Cipher</a>, Cryptologia, Vol. 29, Iss. 1 (2005), pp. 59-72; <a href="http://jeff.over.bz/papers/undergrad/on-the-keyspace-of-the-hill-cipher.pdf">author's copy</a>.
%F A052497 a(n) = (9^n - 1)*(9^n - 9)*...*(9^n - 9^(n-1)).
%F A052497 a(n) = A053764(n)*A027877(n). - _Bruno Berselli_, Jan 30 2013
%F A052497 a(n) ~ c * 9^(n^2), where c = A132037. - _Amiram Eldar_, Jul 06 2025
%t A052497 Table[Product[(9^n - 9^j), {j, 0, n-1}], {n, 0, 10}] (* _G. C. Greubel_, May 14 2019 *)
%o A052497 (Magma) [1] cat [&*[(9^n - 9^k): k in [0..n-1]]: n in [1..10]]; // _Bruno Berselli_, Jan 28 2013
%o A052497 (PARI) {a(n) = prod(j=0,n-1, 9^n - 9^j)}; \\ _G. C. Greubel_, May 14 2019
%o A052497 (Sage) [product(9^n - 9^j for j in (0..n-1)) for n in (0..10)] # _G. C. Greubel_, May 14 2019
%Y A052497 Cf. A027877, A053764.
%Y A052497 Cf. A002884, A003792, A053290, A053291, A053292, A053293, A052496, A052498, A132037.
%K A052497 nonn,easy
%O A052497 0,2
%A A052497 _Vladeta Jovovic_, Mar 16 2000