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

[John Keith]

(01-18-2019 05:53 AM)Thomas Klemm Wrote:  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

Thanks, Thomas. I know there is a connection here to polynomials and generating functions but this is mostly above my current level of knowledge.