Find Ordinary Generating Function for $k^3 (k \geq 2)$

Question

Could we find the OGF for the sequence $k^3, k \geq 2$?

Yes, tried to differentiate some elementary generating functions... — cinvro, May 05 '14 at 03:27

score 2 · Accepted Answer · edited Apr 13 '17 at 12:20

2

Apply the operator $(xD)^3= (xD)(xD)(xD) $ to $\frac{1}{1-x}$ gives your the answer.

Note:

$$D =\frac{d}{dx}. $$

edited Apr 13 '17 at 12:20

Community

answered May 05 '14 at 03:45

Mhenni Benghorbal

score 1 · Answer 2 · answered May 05 '14 at 03:44

1

Hint: $~k^3x^k=(x\frac{\partial}{\partial x})^3x^k$

answered May 05 '14 at 03:44

anon

2 Answers2