The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065601 Number of Dyck paths of length 2n with exactly 1 hill. 4
 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). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 Naiomi Cameron, J. E. McLeod, Returns and Hills on Generalized Dyck Paths, Journal of Integer Sequences, Vol. 19, 2016, #16.6.1. 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 [math.CO], 2012. - From N. J. A. Sloane, May 09 2012 Sergey Kitaev, Jeffrey Remmel, Mark Tiefenbruck, Quadrant Marked Mesh Patterns in 132-Avoiding Permutations II, Electronic Journal of Combinatorial Number Theory, Volume 15 #A16. (arXiv:1302.2274) FORMULA Reference gives g.f.'s. Conjecture: 2*(n+1)*a(n) +(-3*n+2)*a(n-1) +2*(-9*n+19)*a(n-2) +4*(-2*n+3)*a(n-3)=0. - R. J. Mathar, Dec 10 2013 a(n) ~ 2^(2*n+3) / (27 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 12 2014 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 # second Maple program: series(((1-sqrt(1-4*x))/(3-sqrt(1-4*x)))^2/x, x=0, 30);  # Mark van Hoeij, Apr 18 2013 MATHEMATICA CoefficientList[Series[((1-Sqrt[1-4*x])/(3-Sqrt[1-4*x]))^2/x, {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 12 2014 *) Table[Sum[(-1)^j*(j+1)*(j+2)*Binomial[2*n-1-j, n], {j, 0, n-1}]/(n+1), {n, 0, 30}] (* Vaclav Kotesovec, May 18 2015 *) CROSSREFS 2nd column of A065600. Cf. A000957. Sequence in context: A133453 A085422 A264630 * A284193 A148255 A148256 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 21 06:11 EDT 2021. Contains 345358 sequences. (Running on oeis4.)