The exponential generating function of the number ${\mathcal{T}}_n$ of standard Young tableaux of size n (or the number of involutions of n letters) is known to be $e^{t+\frac{t^2}{2}}$, which coincides with the moment generating function of normal distribution $N(1,1)$. We apply Laplace's method to the moment integral to derive a new asymptotic formula of ${\mathcal{T}}_n$ which is better than the known result. Meanwhile, by using of Can and Joyce's result in 2012, the number ${\mathcal{S}}_n$ of skew product-type standard Young tableaux of size n is derived to be the n-th moment of normal distribution $N(\tau ,\tau )$, where τ is geometric random variable. The generating function and the asymptotic formula of ${\mathcal{S}}_n$ are obtained.

数的指数生成函数 ${\mathcal{吨}}_n$已知大小为n（或n 个字母的对合次数）的标准 Young tableaux 为${\mathrm{电子}}^{吨+\frac{{吨}^2}{2}}$，与正态分布的矩生成函数一致 $N(1,1)$. 我们将拉普拉斯方法应用于矩积分以推导出新的渐近公式${\mathcal{吨}}_n$这比已知的结果要好。同时，利用 Can 和 Joyce 在 2012 年的结果，${\mathcal{秒}}_n$偏斜产品类型标准的大小为n 的Young tableaux导出为正态分布的第n个矩$N(\tau ,\tau )$，其中τ是几何随机变量。的生成函数和渐近公式${\mathcal{秒}}_n$ 获得。