The following is the list of pairs of partitions [mu1,mu2] such that

Psi2(mu1,n,N)/subs(n=n+2,Phi2(mu2,n)) is a constant, followed by that consta\
    nt

                         that happens to be 1/2 so far



`if mu1 and mu2 are, respectively partions of`, 2, `and `, 4, 
`we have the following pairs`


{[[[2], [4]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 3, `and `, 5, 
`we have the following pairs`


{[[[3], [3, 2]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 4, `and `, 6, 
`we have the following pairs`


{}




`if mu1 and mu2 are, respectively partions of`, 5, `and `, 7, 
`we have the following pairs`


{[[[5], [5, 2]], 1/2], [[[3, 2], [4, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 6, `and `, 8, 
`we have the following pairs`


{[[[3, 3], [3, 3, 2]], 1/2], [[[4, 2], [8]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 7, `and `, 9, 
`we have the following pairs`


{[[[7], [7, 2]], 1/2], [[[5, 2], [5, 4]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 8, `and `, 10, 
`we have the following pairs`


{[[[5, 3], [5, 3, 2]], 1/2], [[[3, 3, 2], [4, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 9, `and `, 11, 
`we have the following pairs`


{[[[9], [9, 2]], 1/2], [[[7, 2], [7, 4]], 1/2], [[[3, 3, 3], [3, 3, 3, 2]], 1/2
], [[[4, 3, 2], [8, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 10, `and `, 12, 
`we have the following pairs`


{[[[5, 5], [5, 5, 2]], 1/2], [[[7, 3], [7, 3, 2]], 1/2], [[[5, 3, 2], [5, 4, 3]
], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 11, `and `, 13, 
`we have the following pairs`


{[[[11], [11, 2]], 1/2], [[[9, 2], [9, 4]], 1/2], [[[5, 3, 3], [5, 3, 3, 2]], 1
/2], [[[5, 4, 2], [8, 5]], 1/2], [[[3, 3, 3, 2], [4, 3, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 12, `and `, 14, 
`we have the following pairs`


{[[[7, 5], [7, 5, 2]], 1/2], [[[9, 3], [9, 3, 2]], 1/2], [[[5, 5, 2], [5, 5, 4]
], 1/2], [[[7, 3, 2], [7, 4, 3]], 1/2], [[[3, 3, 3, 3], [3, 3, 3, 3, 2]], 1/2],
[[[4, 3, 3, 2], [8, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 13, `and `, 15, 
`we have the following pairs`


{[[[13], [13, 2]], 1/2], [[[11, 2], [11, 4]], 1/2], [[[5, 5, 3], [5, 5, 3, 2]],
1/2], [[[7, 3, 3], [7, 3, 3, 2]], 1/2], [[[7, 4, 2], [8, 7]], 1/2], [[[5, 3, 3,
2], [5, 4, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 14, `and `, 16, 
`we have the following pairs`


{[[[7, 7], [7, 7, 2]], 1/2], [[[9, 5], [9, 5, 2]], 1/2], [[[11, 3], [11, 3, 2]]
, 1/2], [[[7, 5, 2], [7, 5, 4]], 1/2], [[[8, 4, 2], [16]], 1/2], [[[9, 3, 2], [
9, 4, 3]], 1/2], [[[5, 3, 3, 3], [5, 3, 3, 3, 2]], 1/2], [[[5, 4, 3, 2], [8, 5,
3]], 1/2], [[[3, 3, 3, 3, 2], [4, 3, 3, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 15, `and `, 17, 
`we have the following pairs`


{[[[15], [15, 2]], 1/2], [[[13, 2], [13, 4]], 1/2], [[[5, 5, 5], [5, 5, 5, 2]],
1/2], [[[7, 5, 3], [7, 5, 3, 2]], 1/2], [[[9, 3, 3], [9, 3, 3, 2]], 1/2], [[[9,
4, 2], [9, 8]], 1/2], [[[5, 5, 3, 2], [5, 5, 4, 3]], 1/2], [[[7, 3, 3, 2], [7,
4, 3, 3]], 1/2], [[[3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 2]], 1/2], [[[4, 3, 3, 3, 2
], [8, 3, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 16, `and `, 18, 
`we have the following pairs`


{[[[9, 7], [9, 7, 2]], 1/2], [[[11, 5], [11, 5, 2]], 1/2], [[[13, 3], [13, 3, 2
]], 1/2], [[[7, 7, 2], [7, 7, 4]], 1/2], [[[9, 5, 2], [9, 5, 4]], 1/2], [[[11,
3, 2], [11, 4, 3]], 1/2], [[[5, 5, 3, 3], [5, 5, 3, 3, 2]], 1/2], [[[5, 5, 4, 2
], [8, 5, 5]], 1/2], [[[7, 3, 3, 3], [7, 3, 3, 3, 2]], 1/2], [[[7, 4, 3, 2], [8
, 7, 3]], 1/2], [[[5, 3, 3, 3, 2], [5, 4, 3, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 17, `and `, 19, 
`we have the following pairs`


{[[[17], [17, 2]], 1/2], [[[15, 2], [15, 4]], 1/2], [[[7, 5, 5], [7, 5, 5, 2]],
1/2], [[[7, 7, 3], [7, 7, 3, 2]], 1/2], [[[9, 5, 3], [9, 5, 3, 2]], 1/2], [[[11
, 3, 3], [11, 3, 3, 2]], 1/2], [[[11, 4, 2], [11, 8]], 1/2], [[[5, 5, 5, 2], [5
, 5, 5, 4]], 1/2], [[[7, 5, 3, 2], [7, 5, 4, 3]], 1/2], [[[8, 4, 3, 2], [16, 3]
], 1/2], [[[9, 3, 3, 2], [9, 4, 3, 3]], 1/2], [[[5, 3, 3, 3, 3], [5, 3, 3, 3, 3
, 2]], 1/2], [[[5, 4, 3, 3, 2], [8, 5, 3, 3]], 1/2], [[[3, 3, 3, 3, 3, 2], [4,
3, 3, 3, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 18, `and `, 20, 
`we have the following pairs`


{[[[9, 9], [9, 9, 2]], 1/2], [[[11, 7], [11, 7, 2]], 1/2], [[[13, 5], [13, 5, 2
]], 1/2], [[[15, 3], [15, 3, 2]], 1/2], [[[9, 7, 2], [9, 7, 4]], 1/2], [[[11, 5
, 2], [11, 5, 4]], 1/2], [[[13, 3, 2], [13, 4, 3]], 1/2], [[[5, 5, 5, 3], [5, 5
, 5, 3, 2]], 1/2], [[[7, 5, 3, 3], [7, 5, 3, 3, 2]], 1/2], [[[7, 5, 4, 2], [8,
7, 5]], 1/2], [[[9, 3, 3, 3], [9, 3, 3, 3, 2]], 1/2], [[[9, 4, 3, 2], [9, 8, 3]
], 1/2], [[[5, 5, 3, 3, 2], [5, 5, 4, 3, 3]], 1/2], [[[7, 3, 3, 3, 2], [7, 4, 3
, 3, 3]], 1/2], [[[3, 3, 3, 3, 3, 3], [3, 3, 3, 3, 3, 3, 2]], 1/2], [[[4, 3, 3,
3, 3, 2], [8, 3, 3, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 19, `and `, 21, 
`we have the following pairs`


{[[[19], [19, 2]], 1/2], [[[17, 2], [17, 4]], 1/2], [[[7, 7, 5], [7, 7, 5, 2]],
1/2], [[[9, 5, 5], [9, 5, 5, 2]], 1/2], [[[9, 7, 3], [9, 7, 3, 2]], 1/2], [[[11
, 5, 3], [11, 5, 3, 2]], 1/2], [[[13, 3, 3], [13, 3, 3, 2]], 1/2], [[[13, 4, 2]
, [13, 8]], 1/2], [[[7, 5, 5, 2], [7, 5, 5, 4]], 1/2], [[[7, 7, 3, 2], [7, 7, 4
, 3]], 1/2], [[[8, 5, 4, 2], [16, 5]], 1/2], [[[9, 5, 3, 2], [9, 5, 4, 3]], 1/2
], [[[11, 3, 3, 2], [11, 4, 3, 3]], 1/2], [[[5, 5, 3, 3, 3], [5, 5, 3, 3, 3, 2]
], 1/2], [[[5, 5, 4, 3, 2], [8, 5, 5, 3]], 1/2], [[[7, 3, 3, 3, 3], [7, 3, 3, 3
, 3, 2]], 1/2], [[[7, 4, 3, 3, 2], [8, 7, 3, 3]], 1/2], [[[5, 3, 3, 3, 3, 2], [
5, 4, 3, 3, 3, 3]], 1/2]}




`if mu1 and mu2 are, respectively partions of`, 20, `and `, 22, 
`we have the following pairs`


{[[[11, 9], [11, 9, 2]], 1/2], [[[13, 7], [13, 7, 2]], 1/2], [[[15, 5], [15, 5,
2]], 1/2], [[[17, 3], [17, 3, 2]], 1/2], [[[9, 9, 2], [9, 9, 4]], 1/2], [[[11,
7, 2], [11, 7, 4]], 1/2], [[[13, 5, 2], [13, 5, 4]], 1/2], [[[15, 3, 2], [15, 4
, 3]], 1/2], [[[5, 5, 5, 5], [5, 5, 5, 5, 2]], 1/2], [[[7, 5, 5, 3], [7, 5, 5,
3, 2]], 1/2], [[[7, 7, 3, 3], [7, 7, 3, 3, 2]], 1/2], [[[7, 7, 4, 2], [8, 7, 7]
], 1/2], [[[9, 5, 3, 3], [9, 5, 3, 3, 2]], 1/2], [[[9, 5, 4, 2], [9, 8, 5]], 1/
2], [[[11, 3, 3, 3], [11, 3, 3, 3, 2]], 1/2], [[[11, 4, 3, 2], [11, 8, 3]], 1/2
], [[[5, 5, 5, 3, 2], [5, 5, 5, 4, 3]], 1/2], [[[7, 5, 3, 3, 2], [7, 5, 4, 3, 3
]], 1/2], [[[8, 4, 3, 3, 2], [16, 3, 3]], 1/2], [[[9, 3, 3, 3, 2], [9, 4, 3, 3,
3]], 1/2], [[[5, 3, 3, 3, 3, 3], [5, 3, 3, 3, 3, 3, 2]], 1/2], [[[5, 4, 3, 3, 3
, 2], [8, 5, 3, 3, 3]], 1/2], [[[3, 3, 3, 3, 3, 3, 2], [4, 3, 3, 3, 3, 3, 3]],
1/2]}


                         This took, 7749.679, seconds.