What solution does Maple give to this difference equation?

Question

Here is a set of difference equations for y[n]

62022240 + 545995032 n + 2056791388 n^2 + 4333244560 n^3 + 5587600700 n^4 + 4517982000 n^5 + 2238010000 n^6 + 621200000 n^7 + 74000000 n^8 + (-19027008 - 158454120 n - 566231672 n^2 - 1135130960 n^3 - 1397526400 n^4 - 1082880000 n^5 - 516080000 n^6 - 138400000 n^7 - 16000000 n^8) y[n] + 3 (2 + 5 n) (3 + 5 n)^2 (4 + 5 n) (6 + 5 n) (5 + 6 n) (7 + 6 n) (31 + 20 n) y[1 + n] == 0, y[1] == 158/31

or equivalently

4 (3 + 2 n) (5168520 + n (42053906 + 5 n (28672669 + 5 n (10621126 + 5 n (2308917 + 10 n (147271 + 20 n (2551 + 370 n))))))) + (-8 (1 + n) (3 + 2 n) (8 + 5 n) (7 + 10 n) (9 + 10 n) (11 + 10 n) (13 + 10 n) (11 + 20 n)) y[n] + 3 (2 + 5 n) (3 + 5 n)^2 (4 + 5 n) (6 + 5 n) (5 + 6 n) (7 + 6 n) (31 + 20 n) y[1 + n] == 0, y[1] == 158/31

I would appreciate it if a reader could provide the Maple solution to these equations--as I have been analyzing it with Mathematica, and obtaining a "hypergeometric-rich" solution of large complexity.

Answer 1

Maple doesn't return any hypergeometrics. Its solution has a lot of Gamma functions and a finite summation:

-(3+5*n)*Pi^(1/2)*GAMMA(n+13/10)*GAMMA(n+11/10)*GAMMA(n+9/10)*GAMMA(n+7/10)*GAMMA(n+3/2)*(-cos((1/5)*Pi)+2*cos((1/5)*Pi)^2-1)*64^n*27^(-n)*GAMMA(1+n)*(Sum((4/3)*(cos((1/5)*Pi)+1)*(2*cos((1/5)*Pi)-1)*GAMMA(n1+7/5)*GAMMA(n1+9/5)*GAMMA(n1+11/6)*GAMMA(n1+11/5)*GAMMA(n1+13/6)*GAMMA(n1+8/5)*(2*n1+3)*(9250000*n1^7+63775000*n1^6+184088750*n1^5+288614625*n1^4+265528150*n1^3+143363345*n1^2+42053906*n1+5168520)/(GAMMA(2+n1)*27^(-n1-1)*64^(n1+1)*(2*cos((1/5)*Pi)+1)*(cos((1/5)*Pi)-1)*GAMMA(n1+5/2)*GAMMA(n1+17/10)*GAMMA(n1+19/10)*GAMMA(n1+21/10)*GAMMA(n1+23/10)*Pi^(1/2)*(8+5*n1)*(6*n1+5)*(5*n1+2)*(5*n1+4)*(5*n1+6)*(6*n1+7)*(5*n1+3)^2), n1 = 1 .. n-1)+7900/1287)/((20*n+11)*GAMMA(n+3/5)*GAMMA(n+7/6)*GAMMA(n+6/5)*GAMMA(n+5/6)*GAMMA(n+4/5)*GAMMA(n+2/5)*(cos((1/5)*Pi)+2*cos((1/5)*Pi)^2-1))