Answer
$1+4x+(4x)^2+(4x)^3+(4x)^4$
Work Step by Step
The generating function of $1, 4, 16, 64, 256$ is
$$1+4x+(4x)^2+(4x)^3+(4x)^4$$
or
$$1+4x+16x^2+64x^3+256x^4$$
Discrete Mathematics and Its Applications, Seventh Edition
by Rosen, Kenneth
Published by
McGraw-Hill Education
ISBN 10:
0073383090
ISBN 13:
978-0-07338-309-5
Chapter 8 - Section 8.4 - Generating Functions - Exercises - Page 549: 2
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