(48G/50g) Binomial Transform, Difference Table

[Thomas Klemm]

(01-17-2019 09:56 PM)John Keith Wrote:  A simple modification of the program above will return the inverse binomial transform of the list on level 1:

This can be used to find an explicit formula for a polynomial sequence given only the first couple of values.
From the older thread Solving a Recursive Sequence in Sequence App:

{ 0 1 4 10 20 35 56 }
→
{ 0 1 2 1 0 0 0 }

Thus: \(a_n=0\binom{n}{0}+1\binom{n}{1}+2\binom{n}{2}+1\binom{n}{3}\)

Cheers
Thomas