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A179072 for p == 1 (mod 4).
3

%I #6 Dec 05 2018 08:01:53

%S -2,-32,256,-8192,-262144,5242880,-33554432,-2684354560,8589934592000,

%T 932385860354048,160159261748363264,-1125899906842624,

%U -225179981368524800,5260204364768739328,43977037871723571052544

%N A179072 for p == 1 (mod 4).

%C It appears that a(n) is even.

%t a72[p_] := Module[{k}, k = (p-1)/2; Det @ Table[JacobiSymbol[i+j, p], {i, 1, k}, {j, 1, k}]];

%t a72 /@ Select[Range[1, 201, 4], PrimeQ] (* _Jean-François Alcover_, Dec 05 2018 *)

%Y Cf. A179071, A179072, A179073.

%K sign

%O 1,1

%A _Jonathan Sondow_ and _Wadim Zudilin_, Jun 29 2010