Hello, MATNTRNG!

I hope the is a typo . . .

Crank out the first few terms: .

Take the difference of consecutive terms,

. . then the differences of the differences, and so on.

. .

Since theseconddifferences are constant,

. . the generating function is of theseconddegree, a quadratic.

The general quadratic function is: .

Use the first three values of the function and substitute:

. .

. .

. .

Substitute into [5]: .

Substitute into [3]: .

Therefore, the generating function is: .