eval_when([translate,batch,loadfile],
apply('array,['[sum1,sum2,sum3,dr,sr2,y],30]),
mf(e)::=buildq([e],mode_identity(fixnum,e)),
mdf(e)::=buildq([e],mode_declare(e,fixnum)));

define_variable(z,'z,any);

sum1[k]:=(mdf(k),
block([n:mf(k/2),be,s:0],mdf([n,be]),
          for al:1 thru n-1 do (mdf(al),
            be:n-al,
           s:s+arrayapply('y,[2*al])*arrayapply('y,[2*be])),s));

sum2[k]:=(mdf(k),
block([n:mf(k/2),del,s:0],mdf([n,del]),
      for al:0 thru n do (mdf(al),
      for be:0 thru n-al do (mdf(be),
      for gam:0 thru n-al-be do (mdf(gam),
          del:n-al-be-gam,
  (
 /* check that at least 2 indices are nonzero...must fail
     when at least three are 0. there are 4 cases when three
     indices are 0...and they are test for explicitly...
    the test that all four indices = 0 is redundent. */
    if (al+be+del)*(al+be+gam)*(be+gam+del)*(al+gam+del)=0 then done
     else
     (
           if al+be+gam+del#n then done  else (
        s:s+arrayapply('y,[2*al])*arrayapply('y,[2*be])*
            arrayapply('y,[2*gam])*arrayapply('y,[2*del]))))))),s));

sum3[k]:=(mdf(k),
block([n:mf(k/2),be,s:0],mdf([n,be]),
     for al:1 thru n-2 do (mdf(al),
        be:n-1-al,
     (
    s:s+funmake('e,[0,z])*arrayapply('y,[2*al])*arrayapply('y,[2*be])+
        3/4*arrayapply('dr,[2*al])*arrayapply('dr,[2*be])-
        1/4*(arrayapply('y,[2*al])*arrayapply('dr2,[2*be])+
             arrayapply('dr2,[2*al])*arrayapply('y,[2*be])))),s));

dr[n]:=(mdf(n),diff(arrayapply('y,[n]),z));
dr2[n]:=(mdf(n),diff(arrayapply('dr,[n]),z));
y[n]:=(mdf(n),ratsimp(funmake('e,[0,z])*arrayapply('y,[n-2])-
                      1/4*arrayapply('dr2,[n-2])+
                      1/2*arrayapply('sum1,[n])-1/2*arrayapply('sum2,[n])+
                      1/2*arrayapply('sum3,[n])));