Let the exterior polynomial algebra $A=\Lambda_K[x_1,\ldots,x_n]$ have grading $\deg x_i=d_i$. Is there some nice formula for the Hilbert-Poincare series $HP_A=\sum_k\dim_K \!A_k\,t^k\in\mathbb{Z}[[t]]$ of this algebra?
If $d_1\!=\!\ldots\!=\!d_n\!=\!d$, then $HP_A=\sum_k\binom{n}{k}t^{dk}=(1+t^d)^n$. But I have trouble with the general case.