Problem 6

The sum of the coefficients of all the integrals powers of \(x\) in the expansion of \[{ \left( 1+2\sqrt { x } \right) }^{ 40 }\] If the sum can be represented as \[\frac { 1 }{ A } \left( { 3 }^{ B }+1 \right), \] where \(A, B\) are positive integers less than 100. Find the value of \[A+B+1\]

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