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  "body": "\n## Summary\n\nA linear recurrence with polynomial coefficients relates consecutive terms of a sequence linearly, with coefficients that are polynomials in the index $n$.\nIt generalizes the [[linear recurrences with constant coefficients|0NDVHBVBXB]] and covers many sequences of combinatorics, such as factorials, Catalan numbers and harmonic numbers.\nThe sequences that satisfy such a recurrence are the [[holonomic sequences|NWKX329T01]], and their generating functions are [[holonomic functions|7H44JD9NQD]].\nComputer algebra uses these recurrences as finite descriptions of infinite sequences.\n\n## Explanations\n\n### L1 human\n\nIn the Fibonacci rule $u_{n+2} = u_{n+1} + u_n$, the coefficients are fixed numbers.\nHere the coefficients may grow with $n$, like the factor $n + 1$ in $u_{n+1} = (n+1) u_n$.\nThat rule, started at $u_0 = 1$, produces the factorials $1, 1, 2, 6, 24, \\dots$.\nThe rule is still linear: the terms of the sequence are only multiplied by known quantities and added.\n",
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