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In this paper special values of Bell polynomials are given by using the powerseries solution of the equation $y^{(k)}=e^{ay}$. In addition, complete andpartial exponential autonomous functions, exponential autonomous polynomials,autonomous polynomials and $(k,a)$-autonomous coefficients are defined.Finally, we show the relationship between various numbers countingcombinatorial objects and binomial coefficients, Stirling numbers of the secondkind and autonomous coefficients.

Solution of the Differential Equation $y^{(k)}=e^{ay}$, Special Values of Bell Polynomials and $(k,a)$-Autonomous Coefficients