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I am not sure about you resuest, is the following sufficient for you ?

sage: Gamma = lambda n: sum(gamma^i/factorial(i) for i in range(n))
sage: Gamma(2)
[                     1 sum(z^i*f(i), i, 1, n)]
[sum(z^i*g(i), i, 1, n)                      1]

sage: Gamma(3)
[1/2*sum(z^i*f(i), i, 1, n)*sum(z^i*g(i), i, 1, n) + 1                                sum(z^i*f(i), i, 1, n)]
[                               sum(z^i*g(i), i, 1, n) 1/2*sum(z^i*f(i), i, 1, n)*sum(z^i*g(i), i, 1, n) + 1]

I am not sure about you resuest, your request, is the following sufficient for you ?

sage: Gamma = lambda n: sum(gamma^i/factorial(i) for i in range(n))
sage: Gamma(2)
[                     1 sum(z^i*f(i), i, 1, n)]
[sum(z^i*g(i), i, 1, n)                      1]

sage: Gamma(3)
[1/2*sum(z^i*f(i), i, 1, n)*sum(z^i*g(i), i, 1, n) + 1                                sum(z^i*f(i), i, 1, n)]
[                               sum(z^i*g(i), i, 1, n) 1/2*sum(z^i*f(i), i, 1, n)*sum(z^i*g(i), i, 1, n) + 1]