Archimedes' spheres

Level pending

Archimedes is playing on the beach of Syracuse with an incalculable amount of little spheres of 50 different colors. He also has a huge amount of straw baskets and wants to fill them with his spheres by making all possible combinations of colors and avoiding to put in each basket more than a sphere of the same color. After having done, he writes a number on the sand before leaving. If this number is the totality of spheres he used to fill the baskets, what is the sum of all its digits?

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