https://math.stackexchange.com/a/3871372/230586

3871372_230586.py

from math import comb

# Implementation of DAG counter
def dagcount(n):
    a = {}
    a[0] = 1
    for h in range(1,n+1):
        a[h] = 0
        for k in range(1,h+1):
            a[h] += (-1)**(k+1) * comb(h,k) * 2**(k*(h-k)) * a[h-k]         
    return a
        
# True results
y_true = [
    1,
    1,
    3,
    25,
    543,
    29281,
    3781503,
    1138779265,
    783702329343,
    1213442454842881,
    4175098976430598143,
    31603459396418917607425,
    521939651343829405020504063,
    18676600744432035186664816926721,
    1439428141044398334941790719839535103
    ]

# Predictions
y_pred = dagcount(len(y_true))

# Check predictions against reference
for i in range(len(y_true)):
    print(y_true[i] == y_pred[i])