Geodesic
Enumerating functions for nonnegative integer coordinates of $L$-dimensional vectors
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 147-155

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The enumerating function $C^L(X_1,\dots,X_L)$, which bijectively maps tuples of length $L$ of nonnegative integers to nonnegative integers $Z=C^L(X_1,\dots,X_L)$, is represented as a sum of $L$ figurate numbers. 
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     author = {S. L. Chernyshev},
     title = {Enumerating functions for nonnegative integer coordinates of $L$-dimensional vectors},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {147--155},
     publisher = {mathdoc},
     volume = {15},
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     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a10/}
}
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S. L. Chernyshev. Enumerating functions for nonnegative integer coordinates of $L$-dimensional vectors. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 147-155. http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a10/