Power series factorization tool

This tool factors a truncated power series in the form \[ 1 + \sum_{n=1}^T r(n)q^n = \prod_{n=1}^T (1-q^n)^{-a_n}.\] where equality holds for the coefficients only up to \(q^T\). This is useful for finding patterns in order to conjecture identities of the form \[ 1 + \sum_{n=1}^\infty r(n)q^n = \prod_{n=1}^\infty (1-q^n)^{-a_n}.\]

Enter the series coefficients as a comma-separated list \(1, r(1), r(2), \dots, r(T)\) of integers \(r(n)\).

1, 1, 2, 3, 5, 7, 11