Mathematica 13.2.1 Kernel for Linux x86 (64-bit)
Copyright 1988-2023 Wolfram Research, Inc.

In[1]:= HolonomicFunctions Package version 1.7.3 (21-Mar-2017)
written by Christoph Koutschan
Copyright Research Institute for Symbolic Computation (RISC),
Johannes Kepler University, Linz, Austria
--> Type  ?HolonomicFunctions  for help.

In[2]:=         
Integration 1 took 1.92646s.

Integration 2 took 7.85581s.

Integration 3 took 1758.28s.

Integration 4 took 278.691s.

Integration 5 took 36.9484s.

Integration 6 took 0.503405s.

Out[2]//InputForm= 
-51200*(1 + n)*(2 + n)*(1 + 2*n)*(3 + 2*n)*(5 + 2*n)*(7 + 2*n)*
  (445 + 242*n + 33*n^2)*a[n] + 128*(2 + n)*(3 + 2*n)*(5 + 2*n)*(7 + 2*n)*
  (414370 + 628997*n + 351364*n^2 + 84898*n^3 + 7491*n^4)*a[1 + n] - 
 16*(5 + 2*n)*(7 + 2*n)*(1460132 + 3125336*n + 2775099*n^2 + 1307394*n^3 + 
   344379*n^4 + 48048*n^5 + 2772*n^6)*a[2 + n] - 
 2*(3 + n)*(7 + 2*n)*(3431096 + 6484024*n + 5089654*n^2 + 2124170*n^3 + 
   497179*n^4 + 61886*n^5 + 3201*n^6)*a[3 + n] + 
 (3 + n)*(4 + n)^5*(236 + 176*n + 33*n^2)*a[4 + n]

In[3]:=