## On Claims Derived from Shifted Legendre Polynomial Coefficient Formulas

A few combinatorics arguments... perhaps you can think of some proofs? Hint: I did not approach this via induction proofs:

**General Multiplicative Notions**

Corollary

for and

Corollary

Corollary

Corollary: Binomial Multiplicative Formula

Corollary

**Catalan Numbers**

Corollary

Corollary

Categories: Combinatorics and Probability, Mathematics