{'fraction_non_alphanumeric': 0.02268760907504363, 'fraction_numerical': 0.0017452006980802793, 'mean_word_length': 5.239130434782608, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A new approach for proving or generating combinatorial identities

A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n + 1 arbitrary real parameters. Moreover, this formula enables one not only to prove, but also generate many different combinatorial identities (not being required to know them a priori), simply by assigning adequate values to those parameters. The identities all flow swiftly from one simple theorem and the presentation is self-contained.