The representation of SO(6) is $[i,j,k]$;

The representation of SO(10) is $[i,j,k,m,n]$.

Is there any analytical formula to calculate the dimensions of those representations?

For example,

for SO(6):

dim([1,0,0],D3)=6

dim([0,0,1],D3)=4

dim([0,1,0],D3)=4

dim([0,1,1],D3)=15

dim([0,0,2],D3)=10

dim([i,j,k],D3)=?

for SO(10):

dim([1,0,0,0,0],D5)=10

dim([0,0,0,0,1],D5)=16

dim([0,0,0,1,0],D5)=16

dim([0,0,1,0,0],D5)=120

dim([0,1,0,0,0],D5)=45

dim([i,j,k,m,n],D5)=?