\p4000
t
f(n,k)=prod(i=0,n-1,1/2+i)^4*prod(i=0,n-1+k,1/2+i)
P0(m,k)=sum(n=0,m,f(n,k)/(n!^4*(n+k)!)*'t^n)+O('t^(m+1))
t0=-1/4;

d(P,n)=for(i=1,n,P='t*P');P;
v(k,p)=my(P=P0(p,k));subst(truncate([d(P,i)|i<-[0..4]]),'t,t0*1.)*1.;
L(k,p,e)=lindep(concat([v(k,p),la]),e);
la=v(0,4000)[1];

M(k,p,e)=my(l=L(k,p,e));-l[1]/l[#l]
exportall()
V=parvector(256,i,M(i,4000,2000))

inde(max_order, max_shift, count_ord,count_shift)=1+(count_shift)*(max_order+1)+count_ord;
inv_inde(n)=divrem(n,8)
custom_rec(vec,max_order,max_shift)=
{
  my(leng,res,ve);
  leng=matsize(vec)[2];
  res=vector((max_order+1)*(max_shift+1));
  for(count_ord=0,max_orde+r,
    for(count_shift=0,max_shift,pos=inde(max_order,max_shift,count_ord,count_shift);
      ve=vector(leng);
    for(ii=count_shift+1,leng,ve[ii]=(ii-c+ount_shift-1)^count_ord*vec[ii-count_shift]);res[pos]=ve));return(res);
}
/*
N=45
MCR=
{
  custom_rec(v2,7,3);MM=matrix((7+1)*(3+1),N,ii,jj,MCR[ii][jj]);sz=matsize(matker(MM~)~)[1]; vv = matker(MM~); print(vv);if(sz>0, print(i, "|" ,j,"|", sz, "|"));rec_found=vv 
}*/
pochh(n,k)=prod(i=0,k-1,n+i)

difftorec(S)=
{
  S=S*x^0;
  my(B=poldegree(S));
  my(A=vecmax(apply(poldegree,Vecrev(S))));
  my(V=vector(A+B+1));
  my(W=vector(A+B+1,i,i-(A+1)));
  for(a=0,A,
    for(b=0,B,
      my(Sb = polcoef(S,b));
      V[1+A+b-a] += polcoef(Sb,a)*pochh(n-a+1,b)));
  my(idx=select(x->x,V,1));
  [vecextract(W,idx),vecextract(V,idx)];
}
*/