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For nonnegative integers a and b with a ...

For nonnegative integers a and b with `a +b leq 6`, let `T(a,b)=((6),(a))((6),(b))((6),(a+b))`,=. {where `((n),(r))=nC_r`} Let S denote the sum of all T(a, b), where a and b are nonnegative Integers with `a +b leq 6`. Then the value of S is.

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