A holonomic sequence, also called a P-recursive sequence, is a sequence 
satisfying a linear recurrence
equation
for all sufficiently large 
, where the 
are polynomials and are
not all zero (Stanley 1980, Zeilberger 1990).
Equivalently, the ordinary generating function 
is a holonomic
function. This equivalence allows differential
equations for generating functions and
recurrences with polynomial coefficients
to be translated into one another.
See also
Coefficient,
Differential Equation,
Generating Function,
Holonomic
Function,
Recurrence Equation,
Sequence
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References
Stanley, R. P. "Differentiably Finite Power Series." Europ. J. Combin. 1, 175-188, 1980. https://doi.org/10.1016/S0195-6698(80)80051-5.Zeilberger,
D. "A Holonomic Systems Approach to Special Functions Identities." J.
Comput. Appl. Math. 32, 321-368, 1990. https://doi.org/10.1016/0377-0427(90)90042-X.
Cite this as:
Weisstein, Eric W. "Holonomic Sequence."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HolonomicSequence.html
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