Sum to infinity (3)

\[ 1 + 4x + 10 x^2 + 20 x^3 + 35 x^4 + 56 x^5 + 84 x^6 + 120 x^7 + \cdots \]

Given that the \(n^{\text{th}}\) term after 1 in the sum above is of the form

\[\dfrac{4 \cdot 5 \cdot 6 \cdots ( 4 + (n-1) )}{n!} x^n.\]

Evaluate the sum at \(x= \dfrac 23\).

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