

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
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OFFSET

0,1


COMMENTS

a(n) is the total number of down steps between the first and second up steps in all 4Dyck paths of length 5*(n+1). A 4Dyck 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) 720732; 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



