How to Define a Complete Bell Polynomial in Mathematica?

[anthony2005]

Hello,
how do you define a function or make a list with n elements, where n is any? More precisely there is a function in mathematica, BellY

BellY[n,k,\{x_{1},...x_{n-k+1}\}]

which gives the partial Bell polynomial. I would like to define in mathematica the complete Bell polynomial defined as

CBellY[n,\{x_{1},...x_{n}\}]=\sum_{k=1}^{n}BellY[n,k,\{x_{1},...x_{n-k+1}\}]

How can I do that?
Thank you.

 

[Bill Simpson]

Temporarily I have Mathematica forget it knows BellY so you can see the details.

In[1]:= CBellY[n_,v_]:=Sum[BellY[n,k,Take[v,n-k+1]],{k,1,n}]

In[2]:= CBellY[3,{1,2,3}]

Out[2]= BellY[3,1,{1,2,3}]+BellY[3,2,{1,2}]+BellY[3,3,{1}]

 

[anthony2005]

Great, thank you very much!