> with(SumTools[Hypergeometric]);
[AreSimilar, CanonicalRepresentation, ConjugateRTerm, DefiniteSum, 

  EfficientRepresentation, ExtendedGosper, ExtendedZeilberger, Gosper, 

  IndefiniteSum, IsHolonomic, IsHypergeometricTerm, 

  IsProperHypergeometricTerm, IsZApplicable, KoepfGosper, KoepfZeilberger, 

  LowerBound, MinimalZpair, MultiplicativeDecomposition, PolynomialNormalForm, 

  RationalCanonicalForm, RegularGammaForm, SumDecomposition, Verify, WZMethod, 

  Zeilberger, ZeilbergerRecurrence, ZpairDirect]
> qq:=(7*n)!*(6*n)!*(2*n+k-1)!*(9*n+2*k)!*(10*n+k)!/(2*k!*(5*n)!*(8*n)!*(6*n-k)!^2*(2*n+k)!^2*(n+k)!*(4*n+2*k-1)!);
qq := (factorial(7 n) factorial(6 n) factorial(2 n + k - 1) factorial(9 n

   + 2 k) factorial(10 n + k))//                                             
                               \2 factorial(k) factorial(5 n) factorial(8 n) 

                    2                   2                                     
  factorial(6 n - k)  factorial(2 n + k)  factorial(n + k) factorial(4 n + 2 k

       \
   - 1)/
> q:=(-1)^(n+k)*(10*n+k)!*(9*n+k)!*(8*n+k)!/(k!*(8*n)!^2*(5*n-k)!*(3*n+k)!*(2*n+k)!*(n+k)!);
     /    (n + k)                                                          \/
q := \(-1)        factorial(10 n + k) factorial(9 n + k) factorial(8 n + k)/ 

  /                           2                                       
  \factorial(k) factorial(8 n)  factorial(5 n - k) factorial(3 n + k) 

                                     \
  factorial(2 n + k) factorial(n + k)/
> A:=[8*n+1,7*n+1,10*n+1,9*n+1];
> B:=[1,n+1,2*n+1,15*n+2];
           A := [8 n + 1, 7 n + 1, 10 n + 1, 9 n + 1]
               B := [1, n + 1, 2 n + 1, 15 n + 2]
> R:=(B[4]-A[4]-1)!/((A[1]-B[1])!*(A[2]-B[2])!*(A[3]-B[3])!)*product(t+j,j=B[1]..A[1]-1)*product(t+j,j=B[2]..A[2]-1)*product(t+j,j=B[3]..A[3]-1)/product(t+j,j=A[4]..B[4]-1);
R := (GAMMA(t + 8 n + 1) GAMMA(t + 7 n + 1) GAMMA(t + 10 n + 1) GAMMA(t + 9 n

   + 1))//              2                                                  
         \factorial(8 n)  GAMMA(t + 1) GAMMA(t + n + 1) GAMMA(t + 2 n + 1) 

                     \
  GAMMA(t + 15 n + 2)/
> AA:=[16*n+2,8*n+1,9*n+1,10*n+1];
> BB:=[11*n+2,1,16*n+2,16*n+2];
          AA := [16 n + 2, 8 n + 1, 9 n + 1, 10 n + 1]
            BB := [11 n + 2, 1, 16 n + 2, 16 n + 2]
> RR:=(BB[3]-AA[3]-1)!*(BB[4]-AA[4]-1)!/((AA[1]-BB[1])!*(AA[2]-BB[2])!)*product(2*t+j,j=BB[1]..AA[1]-1)*product(t+j,j=BB[2]..AA[2]-1)/(product(t+j,j=AA[3]..BB[3]-1)*product(t+j,j=AA[4]..BB[4]-1));
RR := (factorial(7 n) factorial(6 n) GAMMA(2 t + 16 n + 2) GAMMA(t + 8 n + 1) 

  GAMMA(t + 9 n + 1) GAMMA(t + 10 n + 1))//                                       
                                          \factorial(5 n) factorial(8 n) GAMMA(2 t

                                               2\
   + 11 n + 2) GAMMA(t + 1) GAMMA(t + 16 n + 2) /
> st:=time():
> IsZApplicable(R,n,t,N,'Z2');
> time()-st;
                              true
                            1879.673
> st:=time():
> IsZApplicable(RR,n,t,N,'Z3');
> time()-st;
                              true
                            6543.069
> st:=time():
> IsZApplicable(q,n,k,N,'Zq');
> time()-st;
                              true
                            1334.379
> st:=time():
> IsZApplicable(qq,n,k,N,'Zqq');
> time()-st;
                              true
                            658.869
> degree(Z2[1],N);
> degree(Z3[1],N);
> degree(Zq[1],N);
> degree(Zqq[1],N);
                               3
                               3
                               3
                               3
> degree(Z2[1],n);
> degree(Z3[1],n);
> degree(Zq[1],n);
> degree(Zqq[1],n);
                              100
                              100
                              100
                              100
> length(lcoeff(Z2[1],[n,N]));
> length(lcoeff(Z3[1],[n,N]));
> length(lcoeff(Zq[1],[n,N]));
> length(lcoeff(Zqq[1],[n,N]));
                              113
                              113
                              113
                              113
> is(Z2[1]=Z3[1]);
> is(Z2[1]=-Zq[1]);
> is(Z2[1]=Zqq[1]);
                              true
                              true
                              true