A054891 - OEIS

%I #6 Jul 10 2011 19:23:53

%S 1,0,0,-56,120,0,0,-240,9,0,0,1440,-1320,0,0,-704,-240,0,0,960,5040,0,

%T 0,-12960,1705,0,0,13440,-3960,0,0,5760,-6480,0,0,-504,-23880,0,0,

%U 23520,16320,0,0,-43680,59400,0,0,-34560,-33551,0,0,-10560,4200,0,0,87360,65520,0,0,-51840,-141240

%N Cusp form of weight 13/2 associated to the unique cusp form of weight 12 under Shimura correspondence.

%D W. Kohnen and D. Zagier, Values of L-series of modular forms at the center of the critical strip. Inv Math. 64 (1981) 175-198

%F See page 177 of reference. Also given by [theta_3(z)^4-(theta_2(z)^4)/8]*theta_3(z)*[(theta_2(z)*theta_4(z))^4]/16.

%o (PARI) {a(n) = local( A, t, T, U); if( n<0, 0, A = x * O(x^n); t = sum( k= 1, sqrtint( n), 2 * x^k^2, 1 + A); T = t^4; U = sum( k= 1, sqrtint( n), 2 * (-1)^k * x^k^2, 1 + A)^4; polcoeff( (7*T + U)/8 * (T - U)/16 * U * t, n))}

%Y Cf. A000594, A192732.

%K sign

%O 1,4

%A Kok seng Chua (chuaks(AT)ihpc.nus.edu.sg), May 23 2000