import math


def vershik_kerov_logan_shepp(n):
    """
    Returns asymptotic value of ℓn for large n.
    For a permutation σ∈Sn, let ℓ(σ) denote the maximal length of an increasing subsequence in σ. 
    Define ℓn = (1/n!) * ∑(σ∈Sn) ℓ(σ),
    the average value of ℓ(σ) for a σ chosen uniformly at random from Sn.

    Parameters
    ----------
    n : int
        denotes n in vershik equation as stated above
    return : float
        returns float number denoting asymptotic value of ℓn.

    """
    if(n != int(n)):
        raise ValueError(
            "n must be integer"
        )
    
    return 2 * math.sqrt(n)