1s1 = 1(1!/1!)
1s2 = 1(2!/2!)
1s3 = 1(3!/3!)
1s4 = 1(4!/4!)
1s5 = 1(5!/5!)
2s1 = 2(1!/1!)
2s2 = 2(2!/2!)+1(2!/1!)
2s3 = 2(3!/3!)+2(3!/2!)
2S4 = 2(4!/4!)+2(4!/3!)+1(4!/2!2!)
2s5 = 2(5!/5!)+4(5!/4!)+1(5!/3!2!)+0(5!/3!)+0(5!/2!2!)+0(5!/2!)+0(5!/1!)
3s1 = 3(1!/1!)
3s2 = 3(2!/2!)+3(2!/1!)
3S3 = 3(3!/3!)+6(3!/2!)+1(3!/1!)
3S4 = 3(4!/4!)+6(4!/3!)+3(4!/2!2!)+3(4!/2!)
3s5 = 3(5!/5!)+X(5!/4!)+X(5!/3!2!)+X(5!/3!)+3(5!/2!2!)+0(5!/2!)+0(5!/1!)
4s1 = 4(1!/1!)
4S2 = 4(2!/2!)+6(2!/1!)
4S3 = 4(3!/3!)+12(3!/2!)+4(3!/1!)
4S4 = 4(4!/4!)+12(4!/3!)+6(4!/2!2!)+12(4!/2!)+1(4!/1!)
4s5 = 4(5!/5!)+X(5!/4!)+X(5!/3!2!)+X(5!/3!)+6(5!/2!2!)+X(5!/2!)+0(5!/1!)
5s1 = 5(1!/1!)
5s2 = 5(2!/2!)+10(2!/1!)
5s3 = 5(3!/3!)+20(3!/2!)+10(3!/1!)
5s4 = 5(4!/4!)+20(4!/3!)+10(4!/2!2!)+39(4!/2!)+1(4!/1!)
5s5 = 5(5!/5!)+X(5!/4!)+X(5!/3!2!)+X(5!/3!)+10(5!/2!2!)+X(5!/2!)+X(5!/1!)