A347281 - OEIS

%I #21 Sep 19 2021 20:46:55

%S 1,2,4,0,36,288,144,18432,11664,115200,144400,0,808151184,133693952,

%T 262440000,299649466368,7937314520976,73575242956800,21204146201616,

%U 6459752448000000,212406372892224,8753824001424826368,195844025123172289600,152252829159294763008,26487254903393025000000

%N a(n) = 2^(n - 1)*permanent(M_n)^2 where M_n is the n X n matrix M_n(j, k) = cos(Pi*j*k/n).

%e a(7) = -3384288*cos(Pi/7) - 3460896*sin(Pi/14) - 45888*cos(2*Pi/7) - 28224*cos(15*Pi/7) + 48384*cos(17*Pi/7) + 1706400 + 3458400*sin(3*Pi/14) = 144. - _Chai Wah Wu_, Sep 19 2021

%o (PARI) P(n)=matpermanent(matrix(n,n,j,k,cos((Pi*j*k)/n)));

%o for(k=1,25,print1(round(2^(k-1)*P(k)^2),", "))

%Y Cf. A085524, A085530, A000169, A085527, A347929.

%K nonn

%O 1,2

%A _Hugo Pfoertner_, Sep 18 2021