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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A124724 a(n) = (4/(n + 1)) * C(5*n, n). 7
4, 10, 60, 455, 3876, 35420, 339300, 3362260, 34179860, 354465254, 3735373880, 39884521950, 430571952300, 4691735290080, 51534335175776, 570003171679020, 6343110854237300, 70968228417131850, 797820661622862900 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the total number of down steps between the first and second up steps in all 4-Dyck paths of length 5*(n+1). A 4-Dyck path is a nonnegative lattice path with steps (1,4), (1,-1) that starts and ends at y = 0. - Sarah Selkirk, May 07 2020

LINKS

Table of n, a(n) for n=0..18.

A. Asinowski, B. Hackl, and S. Selkirk, Down step statistics in generalized Dyck paths, arXiv:2007.15562 [math.CO], 2020.

N. S. S. Gu, H. Prodinger, and S. Wagner, Bijections for a class of labeled plane trees, Eur. J. Combinat. 31 (2010) 720-732; see Theorem 2 with k = 4.

FORMULA

a(n) = C(5*n, n)/(4*n + 1) + 2*C(5*n + 1, n)/(4*n + 2) + 3*C(5*n + 2, n)/(4*n + 3) + 4*C(5*n + 3, n)/(4*n + 4).

PROG

(PARI) a(n) = (4/(n+1)) * binomial(5*n, n); \\ Michel Marcus, May 08 2020

CROSSREFS

Cf. A007226, A007228.

Sequence in context: A328155 A209030 A220824 * A323870 A298162 A203226

Adjacent sequences:  A124721 A124722 A124723 * A124725 A124726 A124727

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 05 2006

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 17 00:35 EDT 2021. Contains 348048 sequences. (Running on oeis4.)