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%I #21 Oct 18 2021 11:17:12
%S 1,27,6291,13589289,266377183929,47123189360124723,
%T 75095231825148137471259,1077370264330489309698453375441,
%U 139124702920688202983704723564457669361
%N Number of n X n invertible matrices A over GF(3) such that A-I is invertible.
%F a(n) = 3^binomial(n,2)*b(n), with b(0)=1, b(n)=(3^n-1)*b(n-1)+(-1)^(n). - _Vladeta Jovovic_, Aug 20 2006
%F From _Geoffrey Critzer_, Oct 17 2021: (Start)
%F Sum_{n>=0} a(n)*u^n/A053290(n) = 1/(1-u)*Product_{r>=1} 1-u/3^r.
%F Limit_{n->inf} a(n)/3^(n^2) = (Product_{r>=1} 1-1/3^r)^2. (End)
%t a[n_] := a[n] = 3^(n-1)*((3^n-1)*a[n-1] + (-1)^n*3^((n-3)*n/2+1)); a[1] = 1; Table[a[n], {n, 1, 9}] (* _Jean-François Alcover_, Jan 12 2012, after formula *)
%Y Cf. A002820.
%K nonn,nice
%O 1,2
%A _Vladeta Jovovic_, Mar 17 2000
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