Vectorization of multifold summation to speedup

I searched this website but didn’t find any suitable answer describing how one can speed up summation in Mathematica using vectorization techniques and other techniques.

I often have to numerically sum over a multi-fold series of the hypergeometric type in my research work. One toy example is

lim = 150; Sum[   Gamma[1 + n1 + n2 + n3]/(n1! n2! n3!) (0.1)^n1 (0.1)^n2 (0.1)^    n3, {n1, 0, lim}, {n2, 0, lim}, {n3, 0, lim}] // AbsoluteTiming 

which takes about 42 sec on my laptop. The only way I know to speed-up is by using ParallelSum instead of Sum, which takes 9 sec, thanks to my 8 core processor. I want to know if there are any tricks or techniques to speed-up?