>>375
f[n_,m_]:=f[n,m]=If[n==1 && 0<m<7,m,If[m<n || m>6n,0,Sum[k*f[n-1,m-k],{k,1,6}]]]

Table[{k,N[f[10,k]/21^10,6]},{k,40,50}]
{{40, 0.0623846}, {41, 0.0712575}, {42, 0.0782634}, {43, 0.0825677}, {44, 0.0835657}, {45, 0.0810097},
{46, 0.0750788}, {47, 0.0663713}, {48, 0.0558120}, {49, 0.0444938}, {50, 0.0334890}}

Table[{k,f[10,k]/21^10},{k,43,45}]//InputForm
{{43, 21860621620/264760015527}, {44, 22124869070/264760015527}, {45, 7149372644/88253338509}}