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In an automatic search, we found conjectural recurrences for some sequences in the OEIS that were not previously recognized as being D-finite.
P. A. MacMahon, Combinatory Analysis
1915
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1941
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H. A. Kramers and G. H. Wannier, Statistics of the two-dimensional ferromagnet. Part II, Phys. Rev
1941
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R. P. Stanley, Differentiably finite power series, European J. Combin
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I. M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A
1990
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D. Zeilberger, A holonomic systems approach to special functions identities, J. Computat. Appl. Math
1990
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M. Bronstein and M. Petkovšek, An introduction to pseudo-linear algebra, Theoret. Comput. Sci
1996
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M. Petkovšek, H. Wilf, and D. Zeilberger, A = B A=B , AK Peters, Ltd., 1997
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R. P. Stanley, Enumerative Combinatorics, Volume 2
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G. E. Andrews, P. Paule, and A. Riese, MacMahon’s partition analysis: The Omega package, European J. Combinat
2001
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P. Flajolet, S. Gerhold, and B. Salvy, On the non-holonomic character of logarithms, powers, and the n n -th prime function, Electron. J. Combin
2005
Cited alongside, same era.
Invited talk
B. Salvy, D-finiteness: algorithms and applications, In Proceedings of ISSAC’05 · 2005
Cited alongside, same era.
M. Kauers, Guessing handbook, Technical Report 09-07, RISC-Linz, 2009
2009
Cited alongside, same era.
https://risc.jku.at/sw/holonomicfunctions/
C. Koutschan, HolonomicFunctions (User’s Guide), Technical Report 10-01, RISC Report Series, Johannes Kepler Universität Linz, Austria, 2010 · 2010
Cited alongside, same era.
W. Hebisch and M. Rubey, Extended Rate, more GFUN, J. Symbolic Comput
2011
Cited alongside, same era.
M. Kauers and P. Paule, The Concrete Tetrahedron
2011
Cited alongside, same era.
A. R. Conway and A. J. Guttmann, On 1324-avoiding permutations, Adv. Appl. Math
2015
Later among the works it cites.
In Handbook of Enumerative Combinatorics
C. Krattenthaler, Lattice path enumeration · 2015
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V. Vatter, Permutation classes, In Handbook of Combinatorics
2015
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A. R. Conway, A. J. Guttmann, and P. Zinn-Justin, 1324-avoiding permutations revisited, Adv. Appl. Math
2018
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C. Axler, On the sum of the first n n prime numbers, J. Théor. Nombres Bordeaux
2019
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https://cs.stanford.edu/~knuth/papers/noncr-conj.pdf
D. E. Knuth, A conjecture about noncrossing paths, 2019 · 2019
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In Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions
M. Kauers, The holonomic toolkit · 2013
Cited alongside, same era.
In Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions
C. Koutschan, Creative telescoping for holonomic functions · 2013
Cited alongside, same era.
F. Chyzak, The ABC of Creative Telescoping—Algorithms, Bounds, Complexity
2014
Cited alongside, same era.
M. Kauers, M. Jaroschek, and F. Johansson, Ore polynomials in Sage, In Computer Algebra and Polynomials
2014
Cited alongside, same era.
N. J. A. Sloane, The on-line encyclopedia of integer sequences, OEIS Foundation Inc., https://oeis.org
Cited in the paper.
A. Bostan, A. E. Price, A. J. Guttmann, and J.-M. Maillard, Stieltjes moment sequences for pattern-avoiding permutations, Electron. J. Combin
2020
Later among the works it cites.
D. Zeilberger, The method of creative telescoping, J. Symbolic Comput
2020
Later among the works it cites.
M. Kauers and C. Koutschan, Guessing with little data, In Proceedings of ISSAC’22
2022
Later among the works it cites.
S. Yurkevich, Personal communication, 2022
2022
Later among the works it cites.