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!)+2(5!/4!)+2(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!)+6(5!/4!)+6(5!/3!2!)+3(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!)+12(5!/4!)+12(5!/3!2!)+12(5!/3!)+12(5!/2!2!)+4(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!)+30(4!/2!)+5(4!/1!)
5s5 = 5(5!/5!)+20(5!/4!)+20(5!/3!2!)+30(5!/3!)+30(5!/2!2!)+20(5!/2!)+1(5!/1!)
nS1 = n(1Pr1)
nS2 = n(2Pr2) + (nC2)(2Pr1)
nS3 = n(3Pr3) + 2(nC2)(3Pr2) + (nC3)(3Pr1)
nS4 = n(4Pr4) + 2(nC2)(4Pr3) + (nC2)(4Pr2r2) + 3(nC3)(4Pr2) + (nC4)(4Pr1)
nS5 = n(5Pr5) + 2(nC2)(5Pr4) + 2(nC2)(5Pr3r2) + 3(nC3)(5Pr3) + 3(nC3)(5Pr2r2) + 4(nC4)(5Pr2) + (nC5)(5Pr1)