A discrete mathematics problem by أحمد الحلاق

Find the sum of the first 55 terms of this sequence

\[ \dbinom 00, \dbinom 10, \dbinom11 , \dbinom20 , \dbinom21 , \dbinom 22 , \dbinom30 , \ldots \]

\[\] Notation: \( \dbinom MN \) denotes the binomial coefficient, \( \dbinom MN = \dfrac{M!}{N!(M-N)!} \).

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