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 A065601 Number of Dyck paths of length 2n with exactly 1 hill. 3
 0, 1, 0, 2, 4, 13, 40, 130, 432, 1466, 5056, 17672, 62460, 222853, 801592, 2903626, 10582816, 38781310, 142805056, 528134764, 1960825672, 7305767602, 27307800400, 102371942932, 384806950624, 1450038737668, 5476570993440, 20727983587220, 78606637060012 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Convolution of A000957(n) with itself gives a(n-1). REFERENCES E. Deutsch, Dyck path enumeration, Discrete Math., 204 (1999) 167-202. E. Deutsch and L. Shapiro, A survey of the Fine numbers, Discrete Math., 241 (2001), 241-265. S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, Arxiv preprint arXiv:1201.6243, 2012. - From N. J. A. Sloane, May 09 2012 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 FORMULA Reference gives g.f.'s. MAPLE b:= proc(x, y, h, z) option remember;      `if`(x<0 or y b(n\$2, true\$2): seq (a(n), n=0..30);  # Alois P. Heinz, May 10 2012 series(((1-sqrt(1-4*x))/(3-sqrt(1-4*x)))^2/x, x=0, 30);  - Mark van Hoeij, Apr 18 2013 CROSSREFS 2nd column of A065600. Cf. A000957. Sequence in context: A033091 A133453 A085422 * A148255 A148256 A163136 Adjacent sequences:  A065598 A065599 A065600 * A065602 A065603 A065604 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Dec 02 2001 EXTENSIONS More terms from Emeric Deutsch, Dec 03 2001 STATUS approved

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