All right. I'm just writing this down as I think of it, so there will be bugs, guaranteed. Will test soon.
It doesn't seem like it's possible to get the coefficients in less than O(degree^2) since you need to calculate Y1 at ‘degree+1` points, and each one takes O(degree). So here’s my solution, based on finite differences:
Y₁(-11+cumSum(binomcdf(20,0→E ;21 points, Y₁({-10,-9,...,9,10})
ΔList(Y₁(-11.5+cumSum(binomcdf(21,0→O ;22 points, Y₁({-10.5,-9.5,...,9.5,10.5}), before taking ΔList(
{∟E(11),∟O(11)→C
For(X,10,1,-1
ΔList(ΔList(∟E→E
Ans(X)→∟C(1+dim(∟C
ΔList(ΔList(∟O→O
Ans(X)→∟C(1+dim(∟C
End
∟C/cumSum(binomcdf(21,0))!