Geodesic
Asymptotics of the Number of Repetition-Free Boolean Functions in the Elementary Basis
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 822-828

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In this paper, we obtain an asymptotic approximation of the number $K_n$ of repetition-free Boolean functions of $n$ variables in the elementary basis $\{\,\vee,-\}$ as $n\to\infty$ with relative error $O(1/\sqrt n\,)$. As a consequence, we verify conjectures on the existence of constants $\delta$ and $\alpha$ such that $$ K_n\sim\delta\cdot\alpha^{n-1}\cdot(2n-3)!!, $$ and obtain these constants.
Keywords: repetition-free Boolean function, Euler number, Stirling number of the second kind, improper integral, two-pole serial set. 
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     author = {O. V. Zubkov},
     title = {Asymptotics of the {Number} of {Repetition-Free} {Boolean} {Functions} in the {Elementary} {Basis}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {822--828},
     publisher = {mathdoc},
     volume = {82},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a2/}
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O. V. Zubkov. Asymptotics of the Number of Repetition-Free Boolean Functions in the Elementary Basis. Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 822-828. http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a2/