%I #10 Oct 25 2014 05:20:56
%S 0,1,1,-8,10,-24,17,84,25,24,115,-144,170,-224,98,32,244,654,803,-560,
%T 916,-616,-109,96,-152,312,913,-1120,2238,-1440,2051,5456,1012,-272,
%U 2438,-288,1162,-2888,2596,96,5864,1008,3315,-4048,3840,-3680,-155,576,1713,16700,8838,-5200,3166
%N Sum_{k=1..n-1} J(2*n,k)*k^2, where J(i,j) is the Jacobi symbol.
%C Suggested by a formula in Petersson.
%D H. Petersson, Modulfunktionen und Quadratische Formen, Springer-Verlag, 1982; p. 98.
%t Table[Sum[JacobiSymbol[2n, k] k^2, {k, 1, n - 1}], {n, 50}] (* _Alonso del Arte_, Oct 24 2014 *)
%o (PARI) a(n)=sum(k=1,n-1,kronecker(2*n,k)*k^2); \\ _Joerg Arndt_, Oct 25 2014
%Y Cf. A097541-A097544.
%K sign
%O 1,4
%A _N. J. A. Sloane_, Aug 27 2004