%I #10 Nov 07 2022 02:22:25

%S 1,12,1320,1742400,25721308800,4145554781913600,

%T 7338585441586912128000,142998501741091915820267520000,

%U 30655092458961006120118267244605440000,72283553302207308288060341547889057722286080000

%N a(n) = (1/2) * (number of n X n 0..10 matrices with MM' mod 11 = I).

%C Also, number of n X n orthogonal matrices over GF(11) with determinant 1. - _Max Alekseyev_, Nov 06 2022

%H Jessie MacWilliams, <a href="https://doi.org/10.2307/2317262">Orthogonal Matrices Over Finite Fields</a>, The American Mathematical Monthly 76:2 (1969), 152-164.

%F a(2k+1) = 11^k * Product_{i=0..k-1} (11^(2k) - 11^(2i)); a(2k) = (11^k + (-1)^(k+1)) * Product_{i=1..k-1} (11^(2k) - 11^(2i)) (see MacWilliams, 1969). - _Max Alekseyev_, Nov 06 2022

%o (PARI) { a071309(n) = my(t=n\2); prod(i=0, t-1, 11^(2*t)-11^(2*i)) * if(n%2, 11^t, 1/(11^t+(-1)^t)); } \\ _Max Alekseyev_, Nov 06 2022

%Y Cf. A071302, A071303, A071304, A071305, A071306, A071307, A071308, A071310.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jun 11 2002

%E Terms a(6) onward from _Max Alekseyev_, Nov 06 2022