A Power Series
whose Coefficients give the Sequence , , ....
(Wolfram Research, Champaign, IL) function DiscreteMath`RSolve`PowerSum
gives the generating function of a given expression, and ExponentialPowerSum gives the exponential generating function.
Generating functions for the first few powers are
See also Moment-Generating Function, Recurrence Relation
Wilf, H. S. Generatingfunctionology, 2nd ed. New York: Academic Press, 1990.
© 1996-9 Eric W. Weisstein