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@article {AdNilIdeals,
    AUTHOR = {Andrews, G.E. and Krattenthaler, C. and Orsina,
              L. and Papi, P.},
     TITLE = {ad-nilpotent {$\mathfrak b$}-ideals in {${\rm sl}(n)$} having a
              fixed class of nilpotence: combinatorics and enumeration},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {354},
      YEAR = {2002},
    NUMBER = {10},
     PAGES = {3835--3853},
   MRCLASS = {17B20 (05A15)},
  MRNUMBER = {1926854},
MRREVIEWER = {Jorge A. Vargas},
       DOI = {10.1090/S0002-9947-02-03064-7},
}

@article {CatPerm,
    AUTHOR = {Barcucci, E. and Del Lungo, A. and Pergola, E. and
              Pinzani, R.},
     TITLE = {From {M}otzkin to {C}atalan permutations},
      NOTE = {Formal power series and algebraic combinatorics (Vienna,
              1997)},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {217},
      YEAR = {2000},
    NUMBER = {1-3},
     PAGES = {33--49},
   MRCLASS = {05A05 (05A15)},
  MRNUMBER = {1766258},
MRREVIEWER = {Stanley Gill Williamson},
       DOI = {10.1016/S0012-365X(99)00254-X},
}

@article {DBKR,
    AUTHOR = {de Bruijn, N.G. and Knuth, D.E. and Rice, S.O.},
     TITLE = {The average height of planted plane trees},
      Note = {\em Graph theory and computing},
     PAGES = {15--22},
 PUBLISHER = {Academic Press, New York},
      YEAR = {1972},
   MRCLASS = {05C05},
  MRNUMBER = {0505710},
MRREVIEWER = {P. E. O'Neil},
}

@article {Flajolet,
    AUTHOR = {Flajolet, P.},
     TITLE = {Combinatorial aspects of continued fractions},
   JOURNAL = {Discrete Math.},
  FJOURNAL = {Discrete Mathematics},
    VOLUME = {32},
      YEAR = {1980},
    NUMBER = {2},
     PAGES = {125--161},
   MRCLASS = {05A10 (05A15 30B70)},
  MRNUMBER = {592851},
MRREVIEWER = {L. Carlitz},
       DOI = {10.1016/0012-365X(80)90050-3},
}

@book {Haglund,
    AUTHOR = {Haglund, J.},
     TITLE = {The {$q$},{$t$}-{C}atalan numbers and the space of diagonal
              harmonics},
    SERIES = {University Lecture Series},
    VOLUME = {41},
      NOTE = {With an appendix on the combinatorics of Macdonald
              polynomials},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2008},
     PAGES = {viii+167},
   MRCLASS = {05E05 (05A05 05A30 33D52)},
  MRNUMBER = {2371044},
MRREVIEWER = {Michael A. Zabrocki},
}

@article {CatMod,
    AUTHOR = {Hein, N. and Huang, J.},
     TITLE = {Modular {C}atalan numbers},
   JOURNAL = {European J. Combin.},
  FJOURNAL = {European Journal of Combinatorics},
    VOLUME = {61},
      YEAR = {2017},
     PAGES = {197--218},
   MRCLASS = {05A19 (05A10)},
  MRNUMBER = {3588717},
       DOI = {10.1016/j.ejc.2016.11.004},
}

@article{Kreweras,
author = {Kreweras, G.},
journal = {Cahiers du Bureau universitaire de recherche op{\'e}rationnelle S{\'e}rie Recherche},
pages = {3-41},
publisher = {Institut Henri Poincar{\'e} - Institut de Statistique de l'Universit{\'e} de Paris},
title = {Sur les {\'e}ventails de segments},
url = {http://eudml.org/doc/272576},
volume = {15},
year = {1970},
}

@article {WeakComp,
    AUTHOR = {Janji\'c, M. and Petkovi\'c, B.},
     TITLE = {A counting function generalizing binomial coefficients and
              some other classes of integers},
   JOURNAL = {J. Integer Seq.},
  FJOURNAL = {Journal of Integer Sequences},
    VOLUME = {17},
      YEAR = {2014},
    NUMBER = {3},
     PAGES = {Article 14.3.5, 23 pp.},
   MRCLASS = {05A10 (05A15 05A19 11B65)},
  MRNUMBER = {3168687},
MRREVIEWER = {Y. H. Harris Kwong},
       URL =
       {https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html}
}

@article {KRT12,
    AUTHOR = {Kitaev, S. and Remmel, J. and Tiefenbruck, M.},
     TITLE = {Quadrant marked mesh patterns in 132-avoiding permutations},
   JOURNAL = {Pure Math. Appl. (PU.M.A.)},
  FJOURNAL = {Pure Mathematics and Applications. PU.M.A.},
    VOLUME = {23},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {219--256},
   MRCLASS = {05E05 (05A05 05A15)},
  MRNUMBER = {3119706},
MRREVIEWER = {Antonio Bernini},
}

@article {Lord,
    AUTHOR = {Lord, N.J.},
     TITLE = {Non-{A}ssociative {O}perations},
   JOURNAL = {Math. Mag.},
  FJOURNAL = {Mathematics Magazine},
    VOLUME = {60},
      YEAR = {1987},
    NUMBER = {3},
     PAGES = {174--177},
   MRCLASS = {DML},
  MRNUMBER = {1572660},
       URL = {http://www.jstor.org/stable/2689567?origin=pubexport},
}

@book{OEIS,
    AUTHOR = {N.J.A. Sloane},
    TITLE = {The On-Line Encyclopedia of Integer Sequences},
    PUBLISHER = {https://oeis.org},
    Yeas = {2017},
}

@article {Shapiro,
    AUTHOR = {Shapiro, L.W.},
     TITLE = {Upper triangular rings, ideals, and {C}atalan numbers},
   JOURNAL = {Amer. Math. Monthly},
  FJOURNAL = {The American Mathematical Monthly},
    VOLUME = {82},
      YEAR = {1975},
     PAGES = {634--637},
   MRCLASS = {05A15 (10M20)},
  MRNUMBER = {0369091},
MRREVIEWER = {R. C. Mullin},
       DOI = {10.2307/2319698},
}

@book {EC2,
    AUTHOR = {Stanley, R.P.},
     TITLE = {Enumerative combinatorics. {V}ol. 2},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {62},
      NOTE = {With a foreword by Gian-Carlo Rota and appendix 1 by Sergey
              Fomin},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1999},
     PAGES = {xii+581},
   MRCLASS = {05A15 (05-02 05E05 05E10 68R05)},
  MRNUMBER = {1676282},
MRREVIEWER = {Ira Gessel},
       DOI = {10.1017/CBO9780511609589},
       URL = {http://dx.doi.org/10.1017/CBO9780511609589},
}

@book {StanleyCatalan,
    AUTHOR = {Stanley, R.P.},
     TITLE = {Catalan numbers},
 PUBLISHER = {Cambridge University Press},
      YEAR = {2015},
     PAGES = {viii+215},
   MRCLASS = {05-01 (01A05 11B75 11B83)},
  MRNUMBER = {3467982},
MRREVIEWER = {David Callan},
       URL = {http://dx.doi.org/10.1017/CBO9781139871495},
}

@book {Monoid,
    AUTHOR = {Steinberg, B.},
     TITLE = {Representation theory of finite monoids},
    SERIES = {Universitext},
 PUBLISHER = {Springer, Cham},
      YEAR = {2016},
     PAGES = {xxiv+317},
   MRCLASS = {20-02 (20M10 20M18 20M25 20M30 20M50 60J05)},
  MRNUMBER = {3525092},
MRREVIEWER = {Volodymyr Mazorchuk},
       DOI = {10.1007/978-3-319-43932-7},
}

@article {Takacs,
    AUTHOR = {Tak\'acs, L.},
     TITLE = {Enumeration of rooted trees and forests},
   JOURNAL = {Math. Sci.},
  FJOURNAL = {The Mathematical Scientist},
    VOLUME = {18},
      YEAR = {1993},
    NUMBER = {1},
     PAGES = {1--10},
   MRCLASS = {05C05 (05C30)},
  MRNUMBER = {1227236},
MRREVIEWER = {J. W. Moon},
}