Simple Python script utilizing power series expansion of the ordinary generating function to compute the sequence terms.

gf_gen.py

import sympy as sp

def generate_sequence(gen_func, num_terms):
    """
    Generates a sequence up to num_terms terms using the given generating function.

    Args:
        gen_func: The generating function as a SymPy expression.
        num_terms (int): The number of terms in the sequence.

    Returns:
        list: A list of integers representing the generated sequence.
    """
    x = sp.symbols('x')
    series_expansion = sp.sympify(gen_func).series(x, 0, num_terms).removeO()
    sequences = list(series_expansion.as_coefficients_dict().values())
    return sequences

def print_sequence(oeis_id, name, length,  generating_function):
    """
    Prints a sequence generated from a given generating function.

    Args:
        generating_function (str): The generating function as a string.
        length (int): The length of the sequence to generate.
        name (str): The name of the sequence.
        oeis_id (str): The OEIS identifier for the sequence.

    Returns:
        None
    """
    sequence = generate_sequence(generating_function, length)
    print(f"\n{name} (OEIS {oeis_id}):\n", sequence)

if __name__ == "__main__":
    sequences = [
        {"oeis_id": "A000012", "name": "All 1's Sequence", "length": 90, "generating_function": '1/(1-x)'},
        {"oeis_id": "A000032", "name": "Lucas Sequence", "length": 39, "generating_function": '(2-x)/(1-x-x^2)'},
        {"oeis_id": "A000045", "name": "Fibonacci Sequence", "length": 41, "generating_function": 'x/(1-x-x**2)'},
        {"oeis_id": "A000108", "name": "Catalan Sequence", "length": 31, "generating_function": '(1-sqrt(1-4*x))/(2*x)'},
        {"oeis_id": "A000129", "name": "Pell Sequence", "length": 32, "generating_function": 'x/(1-2*x-x**2)'},
        {"oeis_id": "A168604", "name": "(2**(n-2)-1) Sequence", "length": 36, "generating_function": 'x**3/(1-2*x)/(1-x)'}
    ]

    for sequence in sequences:
        print_sequence(sequence["oeis_id"], sequence["name"], sequence["length"], sequence["generating_function"])