Are you sure about the first rule? It doesn't seem necessary according to https://oeis.org/A014575.
The problem is really fun.
Since I created the problem series and want the Functions I badge, I thought I'd provide the solution that incorporates vampire_factor and are_fangs. Not a great score, but readable!
Sorry, I mean the Magic Numbers badge.
Replace NaNs with the number that appears to its left in the row.
Test for balanced parentheses
Find the sum of the elements in the "second" diagonal
Number of Even Elements in Fibonacci Sequence
Multivariate polynomials - emulate symbolic form
Fangs of a vampire number
Product of two multivariate polynomials
Multivariate polynomials - overload multiplication
Multivariate polynomials - convert monomial form to array
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