User:Bradley Klee/Differentiably Finite

Prospectus

How many of the sequences in OEIS are the coefficients of a differentiably finite power series? This is a difficult question to answer exactly, but we can at least set a lower bound by creating an index of [dfin] sequences. Univariate power series which are differentiably finite are also holonomic, as discussed in Koutschan's Dissertation, so an index of [dfin] sequences may also help generate and prove identities via the Holonomic Systems Approach. In this effort, we first need to find [dfin] sequences and record their Annihilating operators. This additional data makes an entry easily identifiable. An index is still desirable to assist in searching and browsing.

Index to [dfin] Sequences

Core

Many core sequences are also linear recurrences with constant coefficients: A000032, A000079, A000027, A000035, A000012, A000045, A000124, A000129, A000204, A000217, A000225, A000244, A000290, A000292. Other core sequences are generated as coefficients of a hypergeometric series: A000108. Others have more complicated recurrence equations: A000166, A000262. Note: up to marker (05).

Constant Coefficients

All linear recurrences with constant coefficients are also trivial P-recurrences, thus the generated sequences belong to [dfin]. A quick grep-and-count of the index for constant-coefficient recurrences returns more than 29K hits, i.e. about 10% of the OEIS total up to Jan. 2018.