This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
n(x) is a polynomial with integer coefficients. Proof follows from the recursion P's wiki page.
n(x) is a polynomial with integer coefficients. Proof follows from the recursion P has authored 0 sequences.