OFFSET
0,3
COMMENTS
See Novelli-Thibon (2014) for precise definition.
LINKS
J.-C. Novelli and J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014-202. See Fig. 23.
Jun Yan, Results on pattern avoidance in parking functions, arXiv preprint arXiv:2404.07958 [math.CO], 2024. See Theorem 4.4.
FORMULA
a(n) = Sum_{i=0..n} Sum_{j=0..i} (-2)^(n-i)*binomial(i,j)*binomial(5i+j, n)*binomial(n+1,i)/(n+1) (conjectured). - Michael D. Weiner, May 25 2017
From Jun Yan, Apr 13 2024: (Start)
a(n) = (1/n) * Sum_{k=1..n} binomial(5*n, k - 1) * binomial(n, k)*2^(k - 1) for n > 0.
Let D(n) be the set of 5-Dyck paths that have n up-steps of size 5 and 5n down-steps of size 1 and never go below the x-axis. For every d in D(n), let peak(d) be the number of peaks in d. Then a(n) = Sum_{d in D(n)} 2^(peak(d) - 1). (End)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 14 2014
EXTENSIONS
More terms from Jun Yan, Apr 13 2024
STATUS
approved