OFFSET
0,3
LINKS
Aubrey Blecher and Arnold Knopfmacher, Left to right maxima in Dyck Paths, arXiv:2107.03102 [math.CO], 2021. See Theorem 9 p. 12.
FORMULA
MAPLE
a:= n-> (d-> add((binomial(2*n-1, n-r)-binomial(2*n-1, n-r-1))
*(d(r+2)-d(r)), r=1..n))(numtheory[tau]):
seq(a(n), n=0..27); # Alois P. Heinz, Jul 08 2021
PROG
(PARI) a(n) = sum(r=1, n, (numdiv(r+2)-numdiv(r))*(binomial(2*n-1, n-r)-binomial(2*n-1, n-r-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Jul 08 2021
STATUS
approved