Find the number of ordered sequences of length 100, (d_1, d_2, \dots d_{100}) such that the number of trees with 100 vertices (numbered 1, 2, \dots 100 ) with the degree of vertex i as d_i (for all 1 \leq i \leq 100 ) is maximum possible.
Two degree sequences are considered different if the degree of a vertex in one sequence is different from the corresponding degree in the other. In particular {1, 1, 2} and {1, 2, 1} are considered different.
Two trees are different if there are two vertices (i, j) which are directly connected by an edge in one tree but not in the other. In particular the trees with edges {(1, 2), (2, 3)} and {(1, 3), (3, 2)} are different.
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